Graphing Quadratic Inequalities

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Presentation transcript:

Graphing Quadratic Inequalities

Steps for Graphing (quickly)

Shading

Graph: y ≤ x2 + 6x – 4 * Vertex: (-3,-13) Slope 1, 3, 5 * Solid Line * Less than means shade BELOW

Graph: y > -x2 + 4x – 3 * Vertex: (2, 1) Slope -1, -3, -5 * Dashed Line * Greater than means shade ABOVE

Graph: y ≥ x2 – 8x + 12 * Vertex: (4, -4) Slope 1, 3, 5 * Solid Line * Greater than means shade ABOVE

Graph: y > -x2 + 4x + 5 * Vertex: (2, 9) Slope -1, -3, -5 * Dashed Line * Greater than means shade ABOVE

Solving a Quadratic Inequality

Steps for solving Write the original inequality as an equation Set equal to 0, factor, and solve. > ≥  GREAT OR – or must be in the answer Write the answer

Solve: x2 – 5x ≤ – 4 x2 – 5x = -4 x2 – 5x + 4 = 0 (x – 4) (x – 1) = 0 Answer: 1 ≤ x ≤ 4

Solve: -x2 + 7x < 12 Answer: x < 3 or x > 4 -x2 + 7x = 12

What if it can’t factor? Graph it!

Solve: -(x – 1)2 – 3 < 0 -(x – 1)2 – 3 < y y > -(x – 1)2 – 3 Answer: all real numbers

Solve: x2 + 4 ≤ 0 x2 + 4 ≤ y y ≥ x2 + 4 Answer: no solution