Ch 9: Quadratic Equations F) Graphing Quadratic Inequalities Objective: To graph quadratic inequalities.

Definitions Inequality: Two numbers or expressions that are not “strictly” equal to each other. They are separated by one of these symbols: ≥ (less than) less than (greater than) greater than or equal to or equal to

Rules 1.Graph three points (vertex, left of vertex, right of vertex) (consider the inequality as an equal sign when finding points) 2.Determine if the parabola is solid (≥, ≤) or dashed (>, <) and draw the curve. 3.Choose a “test” point NOT on the parabola and plug it into the inequality. If TRUE then shade the side that includes the test point If FALSE then shade the other side

x y Graph Test Point (0,0) Example 1 Vertex: x = -b 2a = -(0) 2(1) = 0 2 = 0 xy Left Vertex Right Left: Choose x = -2 Right: Choose x = 2 y = (-2) 2 – 5 = -1 y = (2) 2 – 5 = -1 y = (0) 2 − 5 = -5 0 −5−5 −2−2 −1−1 2 −1−1 Test Point: Choose (0,0) 0 ≥ TRUE! ≥ y x 2 − 5

x y Graph Example 2 Vertex: x = -b 2a = -(1) 2(-1) = -2 = 1 2 xy Left Vertex Right Left: Choose x = -1 Right: Choose x = 2 y = -(-1) = -2 y = -(2) = -2 y = -(1/2) 2 + 1/2 = 1/4 1/21/4 −1−1 −2−2 2 −2−2 Test Point: Choose (2,0) 0 > -(2) 2 + 2TRUE! Test Point (2,0) > y -x 2 + x

x y Graph Test Point (0,0) Example 3 y x 2 – 7x + 6 Vertex: x = -b 2a = -(-7) 2(1) = 7 2 = 3.5 xy Left Vertex Right Left: Choose x = 0 Right: Choose x = 7 y = (0) 2 – 7(0) + 6 = 6 y = (7) 2 – 7(7) + 6 = − y =(3.5) 2 −7(3.5)+6= Test Point: Choose (0,0) 0 ≤ (0) 2 − 7(0) + 6TRUE! ≤

x y Graph Example 4 y -x 2 – 2x - 3 Vertex: x = -b 2a = -( − 2) 2( − 1) = 2 − 2 = -1 xy Left Vertex Right Left: Choose x = -3 Right: Choose x = 2 y = -( − 3) 2 − 2( − 3) - 3 = -6 y = -(2) = -2 y = -( − 1) 2 − 2( − 1) − 3 = − 2 −2−2 −3−3 −6−6 2 −2−2 Test Point: Choose (0,0) 0 < -(0) 2 − 2(0) − 3False Test Point (0,0) <

x y Classwork Graph the following inequalities. 1) y ≥ x 2 – 4x + 32) y > -x 2 − 2x − 4 x y

x y 3) y ≥ -2x 2 – 8x − 114) y < x 2 − 2x + 4 x y

x y 5) y > -2x 2 − 4x − 16) y ≤ -x 2 − 4x − 6 x y