1. Linear and Quadratic Functions
Chapter 3
Linear and Quadratic Functions

2. Section 5 Inequalities with Quadratics

3. When solving inequalities, there are no exact answers, there are several answers. Therefore, all answers should be in interval notation.

4. Example 1: Use the graph to solve each inequality
f(x) > 0
f(x) ≤ 0

5. Example 2: Use the graph to solve each inequality a) g(x) ≥ f(x) b) f(x) > g(x)

6. When one side is zero, use x-intercepts to determine which x-values should and shouldn’t be included When both sides are something other than zero, use points of intersections to tell which x’s should be included

7. Given just the inequality  use the calculator to give you a graph and the necessary points 1) If one side is 0 (ex. x2 – 3x – 10 ≤ 0) and one side is an expression, graph y1 = expression, find x-intercepts, and then read the graph according to the given inequality y1 = x2 – 3x – 10 x-intercepts: Where is the graph lower or equal to 0?

8. 2) If one side isn’t zero (ex
2) If one side isn’t zero (ex. x(x – 7) > 8), graph y1 = expression 1 and y2 = expression 2, find intersection and then read the graph according to the given inequality y1 = x(x – 7) y2 = 8 intersection: Where is the left higher than the right?

9. Note: answers should either indicate in between the x-values or less than the x on the left and greater than the x on the right.

10. EXIT SLIP