4.9 Notes – Graph and Solve Quadratic Inequalities

y = ax2 + bx +c y > ax2 + bx +c Don’t shade! Shade up

y < ax2 + bx +c Shade down

Test Point A test point in the area you think you should shade. If you plug it in and it works, then shade that area

1. Sketch the graph of the quadratic inequality using the vertex and intercepts. Then choose a test point and verify your solution. (1,4) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 1 y = 4

x = 1 y = 4 3, -1 3 (1,4) x -3 x 1 -3x + x -(x – 3)(x + 1) = 0 Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 1 x -3 x 1 y = 4 -3x + x 3, -1 -(x – 3)(x + 1) = 0 3 x – 3 = 0 or x + 1 = 0 x = 3 x = -1

x = 1 y = 4 3 (1,4) 3, -1 Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 1 y = 4 3, -1 3

Test Point: (0, 0) Solution

1. Sketch the graph of the quadratic inequality using the vertex and intercepts. Then choose a test point and verify your solution. (-2, -9) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = -2 y = -9

x = -2 y = -9 (-2, -9) x 5 x -1 5x + -x (x + 5)(x – 1) = 0 –5, 1 Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x 5 x = -2 x -1 5x + -x y = -9 (x + 5)(x – 1) = 0 –5, 1 x + 5 = 0 or x – 1 = 0 –5 x = –5 x = 1

y = -9 (-2, -9) x = -2 –5, 1 –5 Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = -2 y = -9 –5, 1 –5

Test Point: (0, 0) Solution

1. Sketch the graph of the quadratic inequality using the vertex and intercepts. Then choose a test point and verify your solution. (-2, -2) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = -2 y = -2

2 2 2 x = -2 2(x2 + 4x + 3) = 0 y = -2 (-2, -2) x 3 x 1 5x + -x –3, –1 Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ 2 2 2 x = -2 2(x2 + 4x + 3) = 0 x 3 y = -2 x 1 5x + -x –3, –1 2(x + 3)(x + 1) = 0 6 x + 3 = 0 or x + 1 = 0 x = –3 x = -1

y = -2 (-2, -2) x = -2 –3, –1 6 Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = -2 y = -2 –3, –1 6

Test Point: (0, 0) Solution

2. Sketch the graph of the quadratic inequality using a table 2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution.

2. Sketch the graph of the quadratic inequality using a table 2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution. x (x,y) (0, 3) (–1, –3) –1 (–2, –5) –2 –3 (–3, –3) –4 (–4, 3)

(0, 3) (–1, –3) (–2, –5) (–3, –3) (–4, 3)

Test Point: (1, 1) Not a Solution

2. Sketch the graph of the quadratic inequality using a table 2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution.

2. Sketch the graph of the quadratic inequality using a table 2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution. x (x,y) (4, 1) 4 (3, 4) 3 (2, 5) 2 1 (1, 4) (0, 1)

(4, 1) (3, 4) (2, 5) (1, 4) (0, 1)

Test Point: (1, 1) Not a Solution

2. Sketch the graph of the quadratic inequality using a table 2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution.

2. Sketch the graph of the quadratic inequality using a table 2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution. x (x,y) (4, -3) 4 (2, 3) 2 (0, 5) -2 (-2, 3) -4 (-4, -3)

(4, -3) (2, 3) (0, 5) (-2, 3) (-4, -3)

Test Point: (0, 0) Solution