1. Aim: How do we solve quadratic inequalities? Do Now: Solve and graph 1) 8|-2x| - 2 > 30 2) -4|-3 + 7x| + 9 ≥ -59 HW #5 – Handout #2,6,12,16,21 (solve and graph on a number line)

2. Quadratics Before we get started let’s review. A quadratic equation is an equation that can be written in the form, where a, b and c are real numbers. In this lesson we are going to discuss quadratic inequalities.

3. Quadratic Inequalities What do they look like? Here are some examples:

4. Steps to solve quadratic inequalities Step 1 Write the inequality so that ax² + bx + c is on the left side of the inequality and zero is on the right side of the inequality. Step 2 Solve the inequality as though it were a quadratic equation (factor). You will get two values (roots) (r₁ & r₂).

5. Step 3 Use the table below to help solve: Quadratic Inequality ax² + bx + c < or ≤ 0ax² + bx + c > or ≥ 0 ConjunctionDisjunction Solution: { x | r₁ < x < r₂ } Solution: { x| x r₂} Step 4 Graph on a number line (like absolute value ineq)

6. Example 1: x² > -x + 6

7. Example 2: 2x² + 5x ≤ 3

8. Try on your own : #1, 5, 22