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Using Boundless Presentations The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. Free to share, print, make copies and changes. Get yours at Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: If you have any questions or problems please
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] Boundless.com/algebra?campaign_content=book_196_ch apter_3&campaign_term=Algebra&utm_campaign=power point&utm_medium=direct&utm_source=boundless Functions, Equations, and Inequalities Linear Equations and Functions Complex Numbers Quadratic Equations, Functions, and Applications Graphs of Quadratic Functions Free to share, print, make copies and changes. Get yours at Further Equation-Solving
] Boundless.com/algebra?campaign_content=book_196_ch apter_3&campaign_term=Algebra&utm_campaign=power point&utm_medium=direct&utm_source=boundless Functions, Equations, and Inequalities (continued) Working with Linear Inequalities Free to share, print, make copies and changes. Get yours at
Linear Equations and Their Applications Zeroes of Linear Functions Formulas and Problem-Solving Linear Equations and Functions Functions, Equations, and Inequalities > Linear Equations and Functions Free to share, print, make copies and changes. Get yours at ct&utm_source=boundless
Linear equations can be expressed in the form: Ax+By+Cz+...=D. Linear equations can contain one or more variables; it's possible for such an equation to include an infinite number of variables. Linear equations can be used to solve for unknowns in any relationship in which all the variables are first order. Linear Equations and Their Applications Free to share, print, make copies and changes. Get yours at /linear-equations-and-their-applications ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Linear Equations and Functions
A zero is a point at which a function's value will be equal to zero. Its coordinates are (x, 0), where x is equal to the zero of the graph. Zeros can be observed graphically or solved for algebraically. A linear function can have zero, one, or infinitely many zeros. If the function is a horizontal line (slope=0), it will have no zero unless its equation is y=0, in which case it will have infinitely many. If the line is non-horizontal, it will have one zero. Zeroes of Linear Functions Free to share, print, make copies and changes. Get yours at /zeroes-of-linear-functions ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Linear Equations and Functions
A linear equation can be used to solve any problem that includes constants and variable(s) of first order. A linear equation can be solved for any one variable provided that the values of all other variables are known. Linear equations can be used to calculate tip, cost of goods, velocity, simple interest, and many more variables. Formulas and Problem-Solving Free to share, print, make copies and changes. Get yours at /formulas-and-problem-solving ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Linear Equations and Functions
The Complex-Number System Addition, Subtraction, and Multiplication Complex Conjugates and Division Complex Numbers Functions, Equations, and Inequalities > Complex Numbers Free to share, print, make copies and changes. Get yours at ct&utm_source=boundless
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit. The real number a of the complex number z = a + bi is called the real part of z, and the real number b is often called the imaginary part. The real part is denoted by Re(z) or ℜ (z), and the imaginary part b is denoted by Im(z) or ℑ (z). The Complex-Number System Free to share, print, make copies and changes. Get yours at number-system ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Functions, Equations, and Inequalities > Complex Numbers
Complex numbers are added by adding the real and imaginary parts of the summands. That is to say: (a + bi) + (c + di) = (a + c) + (b + d)i. Similarly, subtraction is defined by (a + bi) - (c + di) = (a - c) + (b - d)i. The multiplication of two complex numbers is defined by the following formula: (a + bi)(c + di) = (ac - bd) + (bc + ad)i. Addition, Subtraction, and Multiplication Free to share, print, make copies and changes. Get yours at subtraction-and-multiplication ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Addition of complex numbers View on Boundless.com Functions, Equations, and Inequalities > Complex Numbers
The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted z*. The division of two complex numbers is defined in terms of complex multiplication and real division. Where at least one of c and d is non-zero: (a + bi)/(c + di) = (ac + bd)/(c2 + d2) + [(bc - ad)/(c2 + d2)]i. Division can be defined in this way because of the following observation: (a + bi)/(c + di) = [(a + bi)(c - di)]/[(c + di)(c - di)] = (ac + bd)/(c2 + d2) + [(bc - ad)/(c2 + d2)]i. As shown earlier, c - di is the complex conjugate of the denominator c + di. Complex Conjugates and Division Free to share, print, make copies and changes. Get yours at conjugates-and-division ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Complex Numbers
Quadratic Equations and Quadratic Functions Completing the Square The Quadratic Formula The Discriminant Reducing Equations to a Quadratic Applications and Problem-Solving Quadratic Equations, Functions, and Applications Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications Free to share, print, make copies and changes. Get yours at ct&utm_source=boundless
A quadratic function is of the form: [Equation 1] where a is a nonzero constant, b and c are constants of any value, and x is a variable. A quadratic equation is a quadratic function set equal to 0. Quadratic Equations and Quadratic Functions Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications Free to share, print, make copies and changes. Get yours at applications-24/quadratic-equations-and-quadratic-functions ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 1 View on Boundless.com
The shape of a quadratic function is known as a parabola. The solution(s) to a quadratic equation is/are known as its zero(s), or root(s). Quadratic Equations and Quadratic Functions Free to share, print, make copies and changes. Get yours at applications-24/quadratic-equations-and-quadratic-functions ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications
In the form, [Equation 2], h and k are constants and should be found. Completing the Square Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications Free to share, print, make copies and changes. Get yours at applications-24/completing-the-square ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Equation 2 View on Boundless.com
Once a quadratic polynomial is in the form: [Equation 3], one can solve for two values of x (using the positive and negative square roots). Completing the Square Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications Free to share, print, make copies and changes. Get yours at applications-24/completing-the-square ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Equation 3 View on Boundless.com
When a parabola is plotted, h is the x-coordinate of the axis of symmetry, and k is the minimum value (or maximum value, if a < 0) of the quadratic function. Completing the Square Free to share, print, make copies and changes. Get yours at applications-24/completing-the-square ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications
The quadratic formula is: [Equation 4]where a, and b are the coefficients of the x2 and x terms, respectively, in a quadratic equation, and c is the value of the equation's constant. The Quadratic Formula Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications Free to share, print, make copies and changes. Get yours at applications-24/the-quadratic-formula ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Equation 4 View on Boundless.com
If the discriminant (b2-4ac) is equal to zero, both values of x obtained will be the same, real number. If the discriminant is positive, both roots will be distinct and real. If the discriminant is negative, there will be two imaginary roots with i coefficients. The Quadratic Formula Free to share, print, make copies and changes. Get yours at applications-24/the-quadratic-formula ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications
[Equation 5] is the formula for a quadratic expression's discriminant, where Δ is the discriminant, and a, b and c are coefficients from the parent function. The Discriminant Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications Free to share, print, make copies and changes. Get yours at applications-24/the-discriminant ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Equation 5 View on Boundless.com
If Δ is greater than 0, the polynomial has two real, distinct zeros. If Δ is equal to 0, the polynomial has only one real zero. And if Δ is less than 0, the polynomial has no real zeros, only two distinct complex zeros. A zero is the x value whereat the function crosses the x-axis. That is, it is the x- coordinate at which the function's value equals 0. The Discriminant Free to share, print, make copies and changes. Get yours at applications-24/the-discriminant ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications
A biquadratic equation (quartic equation with no terms of odd-degree) has the form [Equation 6]. It can be expressed as: [Equation 7] (where p=x2). Reducing Equations to a Quadratic Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications Free to share, print, make copies and changes. Get yours at applications-24/reducing-equations-to-a-quadratic ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 6 View on Boundless.com Equation 7 View on Boundless.com
The values of p can be found by graphing, factoring, completing the square, or using the quadratic formula. Their square roots (positive and negative) are the values of x that satisfy the original equation. Higher-order equations can be solved by a similar process that involves reducing their exponents. The requirement is that there are two terms of x such that the ratio of the highest exponent of x to the lower is 2:1. Reducing Equations to a Quadratic Free to share, print, make copies and changes. Get yours at applications-24/reducing-equations-to-a-quadratic ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications
The Pythagorean Theorem, [Equation 8]relates the length of the hypotenuse (c) of a right triangle to the lengths of its legs (a and b). Applications and Problem-Solving Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications Free to share, print, make copies and changes. Get yours at applications-24/applications-and-problem-solving ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 8 View on Boundless.com Euclid's Proof of the Pythagorean Theorem View on Boundless.com
Problems involving gravity and projectile motion are typically dependent upon a second-order variable, usually time or initial velocity depending on the relationship. Coulomb's Law, which relates electrostatic force, charge amount and distance between two charged particles, has a second-order dependence on the separation of the particles. Solving for either charge results in a quadratic function. Applications and Problem-Solving Free to share, print, make copies and changes. Get yours at applications-24/applications-and-problem-solving ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Euclid's Proof of the Pythagorean Theorem View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications
Quadratic Functions of the Form f(x) = a(x-h)^2 + k Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is not Equal to 0 Applications Graphs of Quadratic Functions Functions, Equations, and Inequalities > Graphs of Quadratic Functions Free to share, print, make copies and changes. Get yours at ct&utm_source=boundless
If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the equation are called the roots of the equation. The coefficient a controls the speed of increase (or decrease) of the quadratic function from the vertex. The coefficients b and a together control the axis of symmetry of the parabola. The coefficient b alone is the declivity of the parabola as y-axis intercepts. The coefficient c controls the height of the parabola, or more specifically, it is the point where the parabola intercepts the y-axis. Quadratic Functions of the Form f(x) = a(x-h)^2 + k Free to share, print, make copies and changes. Get yours at /quadratic-functions-of-the-form-f-x-a-x-h-2-k ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Graphs of Quadratic Functions
The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis. If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the equation are called the roots of the equation. Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is not Equal to 0 Free to share, print, make copies and changes. Get yours at /quadratic-functions-of-the-form-f-x-ax-2-bx-c-where-a-is-not-equal-to ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Graphs of Quadratic Functions
If several key points on a function are desired, it can become tedious to calculate each algebraically. Rather than calculating each key point of a function, one can find these values by inspection of its graph. Graphs of quadratic functions can be used to find key points in many different relationships, from finance to science and beyond. Applications Free to share, print, make copies and changes. Get yours at /applications ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Graphs of Quadratic Functions
Rational Equations Radical Equations Equations with Absolute Value Further Equation-Solving Functions, Equations, and Inequalities > Further Equation-Solving Free to share, print, make copies and changes. Get yours at ct&utm_source=boundless
You can have multiple values that will satisfy the equations. It is important to check your work to make sure that all the values you find all work for the equations. If you have a rational equation where the denominators are the same, then the numerators must be the same.This gives us a strategy: Find a common denominator, and then set the numerators equal. It is important to write each equation in its simplest form. This means to factor each problem out as much as you possibly can before starting. Rational Equations Free to share, print, make copies and changes. Get yours at equations ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Further Equation-Solving
When solving equations that involve radicals, begin by asking: is there an x under the square root? The answer to this question will determine the way you approach the problem. If there is not an x under the square root—if only numbers are under the radicals—the problem can be solved much the same way as if it had no radicals. However, if there is an x under a square root, then move everything except the radical to one side, then square both sides. Squaring both sides can introduce false answers—so it is important to check the answers after solving! Radical Equations Free to share, print, make copies and changes. Get yours at equations ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Further Equation-Solving
Absolute value is one of the simplest functions—and paradoxically, one of the most problematic. On the face of it, nothing could be simpler: it just means "whatever comes in, a positive number comes out". In order to solve an absolute value equation: 1) Isolate the absolute value algebraically. 2) Think through the problem. That is to say, set the absolute value term equal to the other side of the equation, then the opposite of the other side (-1 times it). 3) Finally, do more algebra to isolate x. Absolute values are always positive. An absolute value equation can have, at most, two solutions. Equations with Absolute Value Free to share, print, make copies and changes. Get yours at with-absolute-value ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Absolute Value View on Boundless.com Functions, Equations, and Inequalities > Further Equation-Solving
Linear Inequalities Compound Inequalities Inequalities with Absolute Value Solving Problems with Inequalities Working with Linear Inequalities Functions, Equations, and Inequalities > Working with Linear Inequalities Free to share, print, make copies and changes. Get yours at ct&utm_source=boundless
When two expressions are connected by [Equation 9]sign, we have an inequality. For inequalities that contain variable expressions, you may be asked to solve the inequality for that variable. This just means that you need to find the values of the variable that make the inequality true. Linear Inequalities Functions, Equations, and Inequalities > Working with Linear Inequalities Free to share, print, make copies and changes. Get yours at /linear-inequalities ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Equation 9 View on Boundless.com Inequality View on Boundless.com
A linear inequality is solved very similarly to how we solve equal functions. The difference the answers are:-[Equation 10],less than the found solution.-[Equation 11],greater than the found solution.-[Equation 12],contains values equal and less than the found solution.-[Equation 13],contains values equal and greater than the found solution. Linear Inequalities Functions, Equations, and Inequalities > Working with Linear Inequalities Free to share, print, make copies and changes. Get yours at /linear-inequalities ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Equation 10 View on Boundless.com Inequality View on Boundless.com Equation 11 View on Boundless.com Equation 12 View on Boundless.com
Linear inequalities are commonly written out as a0 + a1x1 + a2x anxn < 0. Linear Inequalities Free to share, print, make copies and changes. Get yours at /linear-inequalities ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Inequality View on Boundless.com Functions, Equations, and Inequalities > Working with Linear Inequalities
Another type of inequality is the compound inequality. A compound inequality is of the form: a < x < b. There are two statements in a compound inequality. The first statement is a < x. The next statement is x < b. When we read this statement, we say "a is less than x," then continue saying "and x is less than b". An example of a compound inequality is: 4 < x < 9. In other words, x is some number strictly between 4 and 9. Compound Inequalities Free to share, print, make copies and changes. Get yours at /compound-inequalities ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Functions, Equations, and Inequalities > Working with Linear Inequalities
Problems involving absolute values and inequalities can be approached in at least two ways. Inequalities with absolute values can be solved by trial-and-error. Another way to solve inequalities with absolute values is to think of the absolute value as representing distance from 0 and then finding the values that satisfy that condition. Inequalities with Absolute Value Free to share, print, make copies and changes. Get yours at /inequalities-with-absolute-value ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundles s Solution to ∣ x ∣ <10 View on Boundless.com Functions, Equations, and Inequalities > Working with Linear Inequalities
Inequalities can be solved by basically the same methods as linear equations with the exception that multiplication by a negative number reverses the direction of the inequality. Let a, b, and c represent real numbers and assume that a < b. Then, if a < b, a + c < b + c and a − c < b − c; if any real number is added to or subtracted from both sides of an inequality, the sense of the inequality remains unchanged. If c is a positive real number, then if a < b, ac < bc and ac < bc. If both sides of an inequality are multiplied or divided by the same positive number, the sense of the inequality remains unchanged. While, if c is a negative real number, then if a bc and ac > bc. If both sides of an inequality are multiplied or divided by the same negative number, the inequality sign must be reversed in order for the resulting inequality to be equivalent to the original inequality. Solving Problems with Inequalities Free to share, print, make copies and changes. Get yours at /solving-problems-with-inequalities ?campaign_content=book_196_chapter_3&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Solving Linear Inequalities View on Boundless.com Functions, Equations, and Inequalities > Working with Linear Inequalities
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Key terms absolute value For a real number, its numerical value without regard to its sign; formally, -1 times the number if the number is negative, and the number unmodified if it is zero or positive. acceleration The change of velocity with respect to time (can include deceleration or changing direction). biquadratic Of a polynomial expression, involving only the second and fourth powers of a variable, as x4 + 3x Sometimes extended to any expression involving the fourth power of variable (but no higher powers), as x4 − 4x3 + 3x2 − x + 1. complex of a number, of the form a + bi, where a and b are real numbers and i is the square root of −1. complex conjugate Of a complex number x, the complex number \overline x formed by changing the sign of the imaginary part: The complex conjugate of a + bi is a - bi. complex numbers (complex analysis) A number of the form a + bi, where a and b are real numbers and i denotes the imaginary unit compound Anything made by combining several things. conjugate any of a set of irrational or complex numbers that are zeros of the same polynomial with integral coefficients constant An identifier that is bound to an invariant value. denominator The number or expression written below the line in a fraction (thus 2 in ½). Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities
discriminant An expression that gives information about the roots of a polynomial; for example, the expression D = b^2 - 4ac determines whether the roots of the quadratic equation ax^2 + bx + c = 0 are real and distinct (D > 0), real and equal (D = 0) or complex (D < 0). expression An arrangement of symbols denoting values, operations performed on them, and grouping symbols. E.g. (2x+4)/2 imaginary of a number, having no real part; that part of a complex number which is a multiple of the square root of -1. imaginary number a number of the form ai, where a is a real number and i the imaginary unit imaginary unit A complex number, usually denoted with i, that is defined as i^2 = -1 inequality A statement that of two quantities one is specifically less than or greater than another. Symbols: or ≥, as appropriate. line of credit A financial agreement under which a bank or other lender agrees to provide a client with loans of money up to an approved limit during a predefined period. The client may borrow the entire credit amount all at once or in portions during the specified period. linear equation A polynomial equation of the first degree (such as x = 2y - 7). Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities
linear function Any function whose graph is a straight line number line A line that graphically represents the real numbers as a series of points whose distance from an origin is proportional to their value numerator The number or expression written above the line in a fraction (thus 1 in ½). parabola The conic section formed by the intersection of a cone with a plane parallel to a plane tangent to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix). parallelogram a convex quadrilateral in which each pair of opposite edges are parallel and of equal length. pH A measurement of a the acidity of a solution, calculated by -log[H+], where [H+] is the concentration of H+ ions in the solution. principal The money originally invested or loaned, on which basic interest and returns are calculated. quadratic A quadratic polynomial, function or equation. Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities
quadratic A quadratic polynomial, function or equation. quadratic equation A polynomial equation of the second degree. quadratic function any function whose value is the solution of a quadratic polynomial quartic function Any function of a polynomial whose greatest exponent is 4. radical A root (of a number or quantity). rational expression An expression that can be expressed as the quotient of two polynomials. real number An element of the set of real numbers. The set of real numbers include the rational numbers and the irrational numbers, but not all complex numbers. real numbers The smallest set containing all limits of convergent sequences of rational numbers. root the number which,when plugged into the equation, will produce a zero. square The second power of a number, value, term or expression. Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities
velocity A vector quantity that denotes the rate of change of position with respect to time, or a speed with the directional component. vertex A point on the curve with a local minimum or maximum of curvature. y-intercept A point at which a line crosses the y-axis of a Cartesian grid. zero Also known as a root, a zero is an x value at which the function of x is equal to 0. Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities
Interactive Graph: Complex Number Illustration A complex number can be visually represented as a pair of numbers (a,b) forming a vector on the complex plane. "Re" is the real axis, "Im" is the imaginary axis, and "i" is the imaginary unit, satisfying i2= −1. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Complex Number Illustration." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
Addition of complex numbers Addition of two complex numbers can be done geometrically by constructing a parallelogram. Free to share, print, make copies and changes. Get yours at Wikipedia. "Complex number." GNU FDL View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Complex_numberView on Boundless.com Functions, Equations, and Inequalities
Absolute Value The absolute value of a real number may be thought of as its distance from zero. Free to share, print, make copies and changes. Get yours at Wikipedia. "Absolute value." GNU FDL View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Absolute_valueView on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Quadratic Function Graph of a polynomial with the quadratic function. It has a parabolic shape and is of the second order. How would changing the signs (negative/positive) of the equation change the shape of the graph? Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Quadratic Function." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Checking Your Work Graph demonstrating the easy mistake when factoring the denominators and having the resulting graphs $y=3x^2-6x$ and $y=4x^2+24x$ Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Checking Your Work." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Quadratic Equation Graph of a polynomial with the quadratic equation. What are the values for a, b, and c, if the typical form for a quadratic equation is ? Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Quadratic Equation." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Complex Conjugate Geometric representation of z and its conjugate in the complex plane. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Complex Conjugate." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Linear Function Graph A linear function graph of (red) and (blue). Graphically, it can be observed that the equation has a zero at, and that has a zero at. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Linear Function Graph." CC BY-SA f2-b0f a8fd06 View on Boundless.comCC BY-SA 3.0https:// 47f2-b0f a8fd06View on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Standard Polynomial Graph of a standard polynomial,. Different values are used, where a=0.1 (black), 0.3 (blue), 1 (green), and 3 (red). Look how the value of a changes the width of the parabola. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Standard Polynomial." CC BY-SA b754a80d586b View on Boundless.comCC BY-SA 3.0https:// b754a80d586bView on Boundless.com Functions, Equations, and Inequalities
Solving Linear Inequalities Miah was asked to find the values of x that make this inequality true: 2x + 1 ≤ 7. Free to share, print, make copies and changes. Get yours at Connexions. "Solving Linear Inequalities." CC BY View on Boundless.comCC BY 3.0http://cnx.org/content/m19599/latest/View on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Biquadratic Function A graph of the biquadratic equation y=x4-2x2. It has three distinct zeroes that can be found by reducing the terms to quadratic form and finding their square roots. Notice what happens if you add/subtract another quadratic term. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Biquadratic Function." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Projectile Motion Graph showing projectile motion with the equation $y=-\left|x-5\right|^2+25$. Projectile motion is a form of motion where a particle (called a projectile) is thrown obliquely near the earth's surface, and it moves along a curved path under the action of gravity. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Projectile Motion." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
Euclid's Proof of the Pythagorean Theorem Euclid used this diagram to explain how the sum of the squares of the triangle's smaller sides (pink and blue) sum to equal the area of the square of the hypotenuse. Free to share, print, make copies and changes. Get yours at Wikipedia. "Illustration to Euclid's proof of the Pythagorean theorem." CC BY-SA View on Boundless.comCC BY-SA on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Parabolas of Differing Discriminant Values Graph of the quadratic formula, essentially, with varying discriminant values. Note that the function with discriminant (Δ) value greater than 0 crosses the x-axis twice, explaining the two distinct values of zeros obtained from the quadratic formula. When the discriminant value is 0, there is only one point at which the function touches the x-axis; hence there being only one calculable root. And for discriminants less than 0, the functions never touch the x- axis at all, resulting in no real roots, only imaginary ones. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Parabolas of Differing Discriminant Values." CC BY-SA differing-discriminant-values View on Boundless.comCC BY-SA 3.0https:// differing-discriminant-valuesView on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Checking Algebraic Solutions Graph of quadratic equation. This graph shows where the given equation is equal to zero. This is equivalent to showing where. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Checking Algebraic Solutions." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// View on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Differing 'k' Values for Quadratic Function The graph of the function is a parabola shifted upward by k, whose vertex is at (0, k). Differing values include k=0 (black), 5 (blue), 10 (green), and 15 (red). Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Differing 'k' Values for Quadratic Function." CC BY-SA for-quadratic-function View on Boundless.comCC BY-SA 3.0https:// for-quadratic-functionView on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Differing 'h' Values for Quadratic Function The graph of the function is a parabola shifted to the right by h, whose vertex is at (h, 0). Differing values include h=0 (black), 5 (blue), 10 (green), and 15 (red). Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Differing 'h' Values for Quadratic Function." CC BY-SA for-quadratic-function View on Boundless.comCC BY-SA 3.0https:// for-quadratic-functionView on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Differing 'h' and 'k' Values for Quadratic Function The graph of the function is a parabola shifted to the right by h and upward by k and whose vertex is at (h, k). Differing values include k=h=0 (black), 5 (blue), 10 (green), and 15 (red). Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Differing 'h' and 'k' Values for Quadratic Function." CC BY-SA and-k-values-for-quadratic-function View on Boundless.comCC BY-SA 3.0https:// and-k-values-for-quadratic-functionView on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Profit vs. Sales Graph of quadratic equation. Graphical representation of profits versus sales can help one visualize, and thus strategize, accordingly. This can be less time-consuming than performing several calculations. Based on this graph, what price point is most effective for maximum sales? Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Profit vs.Sales." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Gratuity as a Function of Bill Price Graph of gratuity as a function of the price of the bill, y=0.18x, where gratuity of 18%. The dependent variable (y) represents gratuity (tip) as a function of cost of the bill (x) before gratuity. How would the equation change if you wanted to tip 20%? Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Gratuity as a Function of Bill Price." CC BY-SA price View on Boundless.comCC BY-SA 3.0https:// priceView on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Differing 'k' and 'h' Values in Quadratic Functions Graphs of quadratic functions of $0=a(x-h)^2+k$ shifted up and to the right by varying 'k' and 'h' values, where k=h=0 (black), 5 (blue), 10 (green), and 15 (red). Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Differing 'k' and 'h' Values in Quadratic Functions." CC BY-SA values-in-quadratic-functions View on Boundless.comCC BY-SA 3.0https:// values-in-quadratic-functionsView on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Quadratic Function Graph of a polynomial with the quadratic function. Because the value is greater than 0, the function has two distinct, real zeros. The graph of f(x) shows that it clearly has two roots: the function crosses the x-axis at x=-1 and x=2. Plugging these values into the equation, we get. The discriminant is thus 9. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Quadratic Function." CC BY-SA a756-ddebaca96f5e View on Boundless.comCC BY-SA 3.0https:// a756-ddebaca96f5eView on Boundless.com Functions, Equations, and Inequalities
Interactive Graph: Example of a Linear Equation Graph showing an example of two linear equations, (red) and (blue). Imagine these linear equations represent the trajectories of two vehicles. If the drivers want to designate a meeting point, they can algebraically find the point of intersection of the two functions. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Example of a Linear Equation." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// View on Boundless.com Functions, Equations, and Inequalities
Solution to ∣ x ∣ <10 All numbers whose absolute value is less than 10; −10 Free to share, print, make copies and changes. Get yours at Connexions. "Inequalities and Absolute Value Concepts -- Absolute Value Inequalities." CC BY View on Boundless.comCC BY 3.0http://cnx.org/content/m18207/1.2/View on Boundless.com Functions, Equations, and Inequalities
Inequality Solutions to x>4 are graphed on the number line. Free to share, print, make copies and changes. Get yours at Connexions. "Solving Linear Inequalities." CC BY View on Boundless.comCC BY 3.0http://cnx.org/content/m19599/latest/View on Boundless.com Functions, Equations, and Inequalities
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities A taxi in New York City charges a flat fee of $3.50, plus $0.75 for every mile traveled. How much would a 6 mile taxi ride cost? A) $4.50 B) $14.00 C) $8.00 D) $9.50
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities A taxi in New York City charges a flat fee of $3.50, plus $0.75 for every mile traveled. How much would a 6 mile taxi ride cost? A) $4.50 B) $14.00 C) $8.00 D) $9.50
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities A textbook has been marked up 15% and is being sold for $ How much did the store pay the manufacturer for the textbook? A) $62.26 B) $90.28 C) $66.73 D) $63.50
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Find the zero of the following function: y=-2x+4. A) x=-2 B) x=2 C) x=0 D) x=-4
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Find the zero of the following function: y=-2x+4. A) x=-2 B) x=2 C) x=0 D) x=-4
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Which of the following function has no zeros? A) x=7 B) y=7 C) y=7x+2 D) x=7y-2
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Which of the following function has no zeros? A) x=7 B) y=7 C) y=7x+2 D) x=7y-2
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Suppose your restaurant bill comes out to $56.50, and you pay a total of $65.54, including tip. Use the formula G=cXr to find out the percent of the gratuity. A) 18% B) 16% C) 15% D) 20%
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Suppose your restaurant bill comes out to $56.50, and you pay a total of $65.54, including tip. Use the formula G=cXr to find out the percent of the gratuity. A) 18% B) 16% C) 15% D) 20%
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Use the formula distance=rate X time to find out how long it will take to drive 225 miles at an average speed of 50 miles per hour. A) 4.0 hours B) 5.0 hours C) 4.5 hours D) 6.5 hours
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Use the formula distance=rate X time to find out how long it will take to drive 225 miles at an average speed of 50 miles per hour. A) 4.0 hours B) 5.0 hours C) 4.5 hours D) 6.5 hours
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Add: (3 - 5i) + (-4 + 7i)? A) 1 + 2i B) i C) i D) i
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Subtract: (-5 + 3i) - (4 + 7i). A) i B) i C) i D) i
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Multiply: (4 - 5i)(-2 + 7i). A) i B) i C) i D) i
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Multiply: (3 + 4i)(3 - 4i). A) 25 B) i C) i D) -7
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities When two complex conjugates a + bi and a - bi are added, the result is: A) 2bi B) 2a C) 2a+2bi D) -2bi
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities When two complex conjugates a + bi and a - bi are added, the result is: A) 2bi B) 2a C) 2a+2bi D) -2bi
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities When two complex conjugates a + bi and a - bi are multiplied, the result is: A) a2-b2 B) a2+2ab+b2 C) -1 D) a2+b2
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities When two complex conjugates a + bi and a - bi are multiplied, the result is: A) a2-b2 B) a2+2ab+b2 C) -1 D) a2+b2
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Divide 3+2i by 4+6i. A) (12-5i)/26 B) 12i-5 C) 26 D) 24-10i
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Which of the following properties is TRUE about a quadratic function? A) The function y=-x2+2x-2 resembles a U-shape when graphed. B) A quadratic function always has two roots. C) A quadratic function is called a hyperbola. D) A quadratic function is of the second order.
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Which of the following properties is TRUE about a quadratic function? A) The function y=-x2+2x-2 resembles a U-shape when graphed. B) A quadratic function always has two roots. C) A quadratic function is called a hyperbola. D) A quadratic function is of the second order.
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Which of the following equations represents a quadratic function? A) y=5x-7 B) y=x2+5x-7 C) x2+y2=25 D) x2/4-y2/16=0
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Which of the following equations represents a quadratic function? A) y=5x-7 B) y=x2+5x-7 C) x2+y2=25 D) x2/4-y2/16=0
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities The first step when solving x2+4x+1=0 by completing the square is: A) Subtract 1 from both sides. B) Take the square root of both sides. C) Subtract 4 from both sides. D) Make the left side into a binomial squared.
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities The first step when solving x2+4x+1=0 by completing the square is: A) Subtract 1 from both sides. B) Take the square root of both sides. C) Subtract 4 from both sides. D) Make the left side into a binomial squared.
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities In solving the quadratic equation 2x2 - 12x + 13 = 0 by completing the square, which of the following is correct? A) (x - 6)2 = 23 B) (x - 6)2 = 29.5 C) (x - 3)2 = 2.5 D) (x + 3)2 = 2.5
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities In solving the quadratic equation 2x2 - 12x + 13 = 0 by completing the square, which of the following is correct? A) (x - 6)2 = 23 B) (x - 6)2 = 29.5 C) (x - 3)2 = 2.5 D) (x + 3)2 = 2.5
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities The first step when using the quadratic formula to solve 4x2+2x=7 is: A) Divide both sides by 4. B) Subtract 7 from both sides. C) Take the square root of both sides. D) Set a=4, b=2, and c=7.
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities The first step when using the quadratic formula to solve 4x2+2x=7 is: A) Divide both sides by 4. B) Subtract 7 from both sides. C) Take the square root of both sides. D) Set a=4, b=2, and c=7.
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Solve the following using the quadratic formula: x2-4x+4=0. A) x=2 and x=-2 B) x=0 C) x=2 D) x=2 and x=0
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Solve the following using the quadratic formula: x2+2x-8=0. A) x=4 and x=2 B) x=-4 and x=2 C) x=4 and x=-2 D) x=-4 and x=-2
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Solve the following using the quadratic formula: x2+2x-8=0. A) x=4 and x=2 B) x=-4 and x=2 C) x=4 and x=-2 D) x=-4 and x=-2
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities If the value of the discriminant is positive: A) there are two real roots. B) there are two complex roots. C) there is one real root. D) we don't know the nature of the roots.
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities If the value of the discriminant is positive: A) there are two real roots. B) there are two complex roots. C) there is one real root. D) we don't know the nature of the roots.
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities If the value of the discriminant is 0, which of the following could represent possible roots of the function? A) x=1 and x=-1 B) x=1+i and x=1-i C) x=1-i D) x=1
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities If the value of the discriminant is 0, which of the following could represent possible roots of the function? A) x=1 and x=-1 B) x=1+i and x=1-i C) x=1-i D) x=1
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Find the discriminant of the following function: x2+6x+5=0. A) 4 B) -1 C) 16 D) -5
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Find the discriminant of the following function: x2+6x+5=0. A) 4 B) -1 C) 16 D) -5
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities The height, h, in feet of an object above the ground is given by h=-16t2+64t+190, where t is the time in seconds. Find the time it takes the object to strike the ground. A) 5.98 seconds B) 1.98 seconds C) 25.4 seconds D) 8 seconds
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities The height, h, in feet of an object above the ground is given by h=-16t2+64t+190, where t is the time in seconds. Find the time it takes the object to strike the ground. A) 5.98 seconds B) 1.98 seconds C) 25.4 seconds D) 8 seconds
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities The number of bacteria in a refrigerated food is given by N(T)=20T2-20T+120 for − 2 ≤ T ≤14 and where T is the temperature of the food in Celsius. At what temperature will the number of bacteria be minimal? A) 1/2 ºC B) 1 ºC C) 2 ºC D) 0 ºC
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities The number of bacteria in a refrigerated food is given by N(T)=20T2-20T+120 for − 2 ≤ T ≤14 and where T is the temperature of the food in Celsius. At what temperature will the number of bacteria be minimal? A) 1/2 ºC B) 1 ºC C) 2 ºC D) 0 ºC
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities The form f(x)=a(x-h)2+k of the quadratic function is advantageous because: A) it is the only form that can be factored. B) h and k are the x and y coordinates of the vertex. C) it is in standard form. D) h and k are the roots of the function.
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities The form f(x)=a(x-h)2+k of the quadratic function is advantageous because: A) it is the only form that can be factored. B) h and k are the x and y coordinates of the vertex. C) it is in standard form. D) h and k are the roots of the function.
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities A quadratic in standard form can easily be converted into the form f(x)=a(x-h)2+k by: A) using the quadratic formula. B) factoring. C) none of these answers. D) completing the square.
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities A quadratic in standard form can easily be converted into the form f(x)=a(x-h)2+k by: A) using the quadratic formula. B) factoring. C) none of these answers. D) completing the square.
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Which of the following quadratic functions is in standard form? A) y=2(x-9)2+4 B) x(x+6)=3 C) y=3x2+7x-6 D) 4(x2-3x)=5
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Which of the following quadratic functions is in standard form? A) y=2(x-9)2+4 B) x(x+6)=3 C) y=3x2+7x-6 D) 4(x2-3x)=5
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Which of the following statements is TRUE about the following quadratic: y=-2x2+4x+7? A) The discriminant is 72. B) The parabola opens upward. C) The vertex is at x=-1. D) It crosses the x-axis at 1 and -3.
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities Which of the following statements is TRUE about the following quadratic: y=-2x2+4x+7? A) The discriminant is 72. B) The parabola opens upward. C) The vertex is at x=-1. D) It crosses the x-axis at 1 and -3.
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities You decide to start making picture frames. The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm2. The inside of the frame has to be11 cm by 6 cm. What should the width x of the metal be? A) About 9.3 cm B) About 2.8 cm C) About 0.8 cm D) About 1.3 cm
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Functions, Equations, and Inequalities You decide to start making picture frames. The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm2. The inside of the frame has to be11 cm by 6 cm. What should the width x of the metal be? A) About 9.3 cm B) About 2.8 cm C) About 0.8 cm D) About 1.3 cm
Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities A ball is thrown straight up into the air from a height of 3 meters. Its height is modeled by the equation h=-5t2+14t+3, where t is time in seconds. In how many seconds will the ball hit the ground? A) 0.2 seconds B) 5 seconds C) 3 seconds D) 2 seconds
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities Solve for x: |x+2|=7. A) x=-5 and x=9 B) x=47 C) x=5 D) x=5 and x=-9
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities The velocity of an object fired directly upward is V=80-32t, where t is time in seconds. When will the velocity be between 32 and 6 feet per second? A) Between 2.5 and 3.5 seconds after launch. B) Between 1.5 and 2.0 seconds after launch. C) Between 0.5 and 1.5 seconds after launch. D) Between 2.0 and 1.5 seconds after launch.
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Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities In math class, 5 exams are given and an 80% must be achieved to pass. Pam has completed the first 4 exams with scores of 71, 84, 79, and 81. Find the minimal score Pam can make on the fifth exam in order to pass the class. A) 80% B) 85% C) 90% D) 87%
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