Chapter 1: Linear and Quadratic functions By Chris Muffi

1-1 Points and Lines Vocabulary- ◦Coordinates- ordered pair of numbers ◦x-axis- is the horizontal line ◦y-axis- is the vertical line ◦Origin- the x and y- axis point of origin ◦Quadrants- the axis divides them into 4 of them ◦Solution- is an ordered pair of numbers that makes the equation true.

1-1 Formulas to know Mid-Point Formula: M = Distance Formula Ab=

1-1 Example Use A(4, 2), B(2, 10), C(-2, 9), and D(0, 1). A. Show that and bisect each other. B. Show that AC = BC. C. What kind of figure is ABCD? D. Find the length of. E. Find the midpoint of.

1-2 Slope of lines Slope Facts to know ◦Horizontal lines have a slope of zero ◦Vertical lines have no slope ◦Negative slopes fall to the right

Slope-intercept form y= mx + b is slope intercept form

1-3 Equations of Lines Formulas: ◦General Form Ax + By= C ◦Slope intercept Form  y = mx + B ◦Point Slope Form ◦Intercept Form

1-4 Linear Functions and Models Function- describes a dependent relationship between two quantities Linear functions have the form f(x) = mx + B

Domain Domain- is the set of values for which the function is defined. You can think of the domain of a function as the set of input values.

Range The set of output values is called the range of the function.

1-5 Complex Numbers Counting Numbers are 1, 2, 3.. Rational Numbers are ratios of integers, to represent fractional parts of quantities. Irrational Numbers are like these

Complex These numbers are commonly referred to as imaginary numbers. And look like these

Pattern of Imaginary

1-6 Solving Quadratic Equations quadratic equation- equation that can be written in the form where a ≠ 0 Roots ◦A root, or solution, of a quadratic equation is a value of the variable that satisfies the equation.

Completing the Square completing the square- method of transforming a quadratic equation so that one side is a perfect square trinomial Steps: ◦Step 1: Divide both sides by the coefficient of so that will have a coefficient of 1. ◦Step 2: Subtract the constant term from both sides. ◦Step 3: Complete the square. Add the square of one half the coefficient of x to both sides. ◦Step 4: Take the square root of both sides and solve for x.

Quadratic Formula quadratic formula- derived by completing the square.

1-7 Quadratic Functions a ≠ 0, is the set of points (x, y) that satisfies the equation then this graph is a parabola

X and Y- Intercept The y-intercept of a parabola with equation is c. If > 0, there are two x- intercepts. If = 0, there is one x-intercept (at a point where the parabola and the x-axis are tangent to each other). If < 0, there are no x- intercepts.