1. Boundless Lecture Slides Free to share, print, make copies and changes. Get yours at www.boundless.com Available on the Boundless Teaching Platform

2. 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 www.boundless.com 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 email: educators@boundless.com http://boundless.com/teaching-platform

3. Boundless is an innovative technology company making education more affordable and accessible for students everywhere. The company creates the world’s best open educational content in 20+ subjects that align to more than 1,000 popular college textbooks. Boundless integrates learning technology into all its premium books to help students study more efficiently at a fraction of the cost of traditional textbooks. The company also empowers educators to engage their students more effectively through customizable books and intuitive teaching tools as part of the Boundless Teaching Platform. More than 2 million learners access Boundless free and premium content each month across the company’s wide distribution platforms, including its website, iOS apps, Kindle books, and iBooks. To get started learning or teaching with Boundless, visit boundless.com.boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com About Boundless

4. 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 www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/quadratic-equations-and-quadratic-functions-127- 10903?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless Equation 1 View on Boundless.com

6. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/quadratic-equations-and-quadratic-functions-127- 10903?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications

7. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/completing-the-square-128- 5547?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 2 View on Boundless.com

8. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/completing-the-square-128- 5547?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 3 View on Boundless.com

9. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/completing-the-square-128- 5547?campaign_content=book_196_section_24&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

10. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/the-quadratic-formula-129- 5862?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 4 View on Boundless.com

11. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/the-quadratic-formula-129- 5862?campaign_content=book_196_section_24&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

12. [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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/the-discriminant-130- 6109?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 5 View on Boundless.com

13. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/the-discriminant-130- 6109?campaign_content=book_196_section_24&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

14. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/reducing-equations-to-a-quadratic-131- 10906?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless Equation 6 View on Boundless.com Equation 7 View on Boundless.com

15. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/reducing-equations-to-a-quadratic-131- 10906?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications

16. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/applications-and-problem-solving-132- 11087?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless Equation 8 View on Boundless.com Euclid's Proof of the Pythagorean Theorem View on Boundless.com

17. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/quadratic-equations-functions-and- applications-24/applications-and-problem-solving-132- 11087?campaign_content=book_196_section_24&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless Euclid's Proof of the Pythagorean Theorem View on Boundless.com Functions, Equations, and Inequalities > Quadratic Equations, Functions, and Applications

18. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

19. Key terms 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 + 3x2 + 2. Sometimes extended to any expression involving the fourth power of variable (but no higher powers), as x4 − 4x3 + 3x2 − x + 1. 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). 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). 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. velocity A vector quantity that denotes the rate of change of position with respect to time, or a speed with the directional component. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities

20. vertex A point on the curve with a local minimum or maximum of curvature. 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 www.boundless.com Functions, Equations, and Inequalities

21. 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 www.boundless.com Boundless. "Interactive Graph: Quadratic Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-quadratic-function View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-quadratic-functionView on Boundless.com Functions, Equations, and Inequalities

22. 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 www.boundless.com Boundless. "Interactive Graph: Biquadratic Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-biquadratic-function View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-biquadratic-functionView on Boundless.com Functions, Equations, and Inequalities

23. 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 www.boundless.com Boundless. "Interactive Graph: Projectile Motion." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-projectile-motion View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-projectile-motionView on Boundless.com Functions, Equations, and Inequalities

24. 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 www.boundless.com Wikipedia. "Illustration to Euclid's proof of the Pythagorean theorem." CC BY-SA http://en.wikipedia.org/wiki/File:Illustration_to_Euclid%2527s_proof_of_the_Pythagorean_theorem.svg View on Boundless.comCC BY-SA http://en.wikipedia.org/wiki/File:Illustration_to_Euclid%2527s_proof_of_the_Pythagorean_theorem.svgView on Boundless.com Functions, Equations, and Inequalities

25. 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 www.boundless.com Boundless. "Interactive Graph: Parabolas of Differing Discriminant Values." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-parabolas-of- differing-discriminant-values View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-parabolas-of- differing-discriminant-valuesView on Boundless.com Functions, Equations, and Inequalities

26. 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 www.boundless.com Boundless. "Interactive Graph: Differing 'k' and 'h' Values in Quadratic Functions." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-differing-k- values-in-quadratic-functions View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-differing-k- values-in-quadratic-functionsView on Boundless.com Functions, Equations, and Inequalities

27. 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 www.boundless.com Boundless. "Interactive Graph: Quadratic Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-quadratic-function-fcb8f1bb-9ab7-4010- a756-ddebaca96f5e View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-quadratic-function-fcb8f1bb-9ab7-4010- a756-ddebaca96f5eView on Boundless.com Functions, Equations, and Inequalities

28. Free to share, print, make copies and changes. Get yours at www.boundless.com 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 is of the second order. C) A quadratic function always has two roots. D) A quadratic function is called a hyperbola.

29. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ 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 is of the second order. C) A quadratic function always has two roots. D) A quadratic function is called a hyperbola.

30. Free to share, print, make copies and changes. Get yours at www.boundless.com 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

31. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ 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

32. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities The first step when solving x2+4x+1=0 by completing the square is: A) Take the square root of both sides. B) Subtract 4 from both sides. C) Make the left side into a binomial squared. D) Subtract 1 from both sides.

33. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities The first step when solving x2+4x+1=0 by completing the square is: A) Take the square root of both sides. B) Subtract 4 from both sides. C) Make the left side into a binomial squared. D) Subtract 1 from both sides.

34. Free to share, print, make copies and changes. Get yours at www.boundless.com 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

35. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ 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

36. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities The first step when using the quadratic formula to solve 4x2+2x=7 is: A) Subtract 7 from both sides. B) Divide both sides by 4. C) Take the square root of both sides. D) Set a=4, b=2, and c=7.

37. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities The first step when using the quadratic formula to solve 4x2+2x=7 is: A) Subtract 7 from both sides. B) Divide both sides by 4. C) Take the square root of both sides. D) Set a=4, b=2, and c=7.

38. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities Solve the following using the quadratic formula: x2-4x+4=0. A) x=2 B) x=2 and x=-2 C) x=0 D) x=2 and x=0

39. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities Solve the following using the quadratic formula: x2-4x+4=0. A) x=2 B) x=2 and x=-2 C) x=0 D) x=2 and x=0

40. Free to share, print, make copies and changes. Get yours at www.boundless.com 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

41. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ 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

42. Free to share, print, make copies and changes. Get yours at www.boundless.com 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.

43. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ 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.

44. Free to share, print, make copies and changes. Get yours at www.boundless.com 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 C) x=1+i and x=1-i D) x=1-i

45. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ 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 C) x=1+i and x=1-i D) x=1-i

46. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities Find the discriminant of the following function: x2+6x+5=0. A) 4 B) -1 C) -5 D) 16

47. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities Find the discriminant of the following function: x2+6x+5=0. A) 4 B) -1 C) -5 D) 16

48. Free to share, print, make copies and changes. Get yours at www.boundless.com 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) 1.98 seconds B) 5.98 seconds C) 25.4 seconds D) 8 seconds

49. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ 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) 1.98 seconds B) 5.98 seconds C) 25.4 seconds D) 8 seconds

50. Free to share, print, make copies and changes. Get yours at www.boundless.com 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 ºC B) 2 ºC C) 1/2 ºC D) 0 ºC

51. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ 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 ºC B) 2 ºC C) 1/2 ºC D) 0 ºC

52. Attribution Wikipedia. "Completing the square." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Completing_the_squareCC BY-SA 3.0http://en.wikipedia.org/wiki/Completing_the_square Wiktionary. "quadratic equation." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quadratic+equationCC BY-SA 3.0http://en.wiktionary.org/wiki/quadratic+equation Wiktionary. "parabola." CC BY-SA 3.0 http://en.wiktionary.org/wiki/parabolaCC BY-SA 3.0http://en.wiktionary.org/wiki/parabola Wiktionary. "vertex." CC BY-SA 3.0 http://en.wiktionary.org/wiki/vertexCC BY-SA 3.0http://en.wiktionary.org/wiki/vertex Wikipedia. "Quadratic equation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_equationCC BY-SA 3.0http://en.wikipedia.org/wiki/Quadratic_equation Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//algebra/definition/zeroCC BY-SA 3.0http://www.boundless.com//algebra/definition/zero Wiktionary. "parabola." CC BY-SA 3.0 http://en.wiktionary.org/wiki/parabolaCC BY-SA 3.0http://en.wiktionary.org/wiki/parabola Wiktionary. "quadratic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quadraticCC BY-SA 3.0http://en.wiktionary.org/wiki/quadratic Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//algebra/definition/zeroCC BY-SA 3.0http://www.boundless.com//algebra/definition/zero Wiktionary. "discriminant." CC BY-SA 3.0 http://en.wiktionary.org/wiki/discriminantCC BY-SA 3.0http://en.wiktionary.org/wiki/discriminant Wikipedia. "Discriminant." CC BY-SA 3.0 http://en.wikipedia.org/wiki/DiscriminantCC BY-SA 3.0http://en.wikipedia.org/wiki/Discriminant Wikipedia. "Quadratic equation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_equationCC BY-SA 3.0http://en.wikipedia.org/wiki/Quadratic_equation Wikipedia. "Quadratic function." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quadratic_functionCC BY-SA 3.0http://en.wikipedia.org/wiki/Quadratic_function Wiktionary. "quadratic function." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quadratic+functionCC BY-SA 3.0http://en.wiktionary.org/wiki/quadratic+function Wiktionary. "vertex." CC BY-SA 3.0 http://en.wiktionary.org/wiki/vertexCC BY-SA 3.0http://en.wiktionary.org/wiki/vertex Wiktionary. "quadratic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quadraticCC BY-SA 3.0http://en.wiktionary.org/wiki/quadratic Wiktionary. "parabola." CC BY-SA 3.0 http://en.wiktionary.org/wiki/parabolaCC BY-SA 3.0http://en.wiktionary.org/wiki/parabola Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities

53. Wikipedia. "Quartic function." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Quartic_functionCC BY-SA 3.0http://en.wikipedia.org/wiki/Quartic_function Wiktionary. "quartic function." CC BY-SA 3.0 http://en.wiktionary.org/wiki/quartic+functionCC BY-SA 3.0http://en.wiktionary.org/wiki/quartic+function Wiktionary. "biquadratic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/biquadraticCC BY-SA 3.0http://en.wiktionary.org/wiki/biquadratic Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//algebra/definition/zeroCC BY-SA 3.0http://www.boundless.com//algebra/definition/zero Wikipedia. "Projectile motion." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Projectile_motionCC BY-SA 3.0http://en.wikipedia.org/wiki/Projectile_motion Wikipedia. "Pythagorean theorem." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Pythagorean_theoremCC BY-SA 3.0http://en.wikipedia.org/wiki/Pythagorean_theorem Wiktionary. "acceleration." CC BY-SA 3.0 http://en.wiktionary.org/wiki/accelerationCC BY-SA 3.0http://en.wiktionary.org/wiki/acceleration Wiktionary. "velocity." CC BY-SA 3.0 http://en.wiktionary.org/wiki/velocityCC BY-SA 3.0http://en.wiktionary.org/wiki/velocity Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities