1. Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.8 – Graphing and Solving Quadratic Inequalities

2. In this section we will learn how to: Graph quadratic inequalities in two variables Solve quadratic inequalities in one variable

3. 5.8 – Graphing and Solving Quadratic Inequalities You can graph quadratic inequalities in two variables using the same techniques you used to graph linear inequalities in two variables Step 1 – Graph the related quadratic function y = ax 2 + bx + c. Decide if the parabola should be solid or dashed Step 2 – Test a point inside the parabola. Check to see if this point is a solution of the inequality Step 3 – If the point is a solution, shade inside the parabola. If the point is NOT a solution, shade outside the parabola

4. 5.8 – Graphing and Solving Quadratic Inequalities Example 1 Use a table to graph y > x 2 – 3x + 2

5. 5.8 – Graphing and Solving Quadratic Inequalities To solve a quadratic inequality in one variable, you can use the graph of the related function. To solve ax 2 + bx + c < 0, graph y = ax 2 + bx + c. Identify x-values for which the graph lies below the x-axis. For ≤ include the x-intercepts. To solve ax 2 + bx + c > 0, graph y = ax 2 + bx + c. Identify x-values for which the graph lies above the x-axis. For ≥ include the x-intercepts.

6. 5.8 – Graphing and Solving Quadratic Inequalities Example 2 Solve x 2 – 4x + 3 > 0

7. 5.8 – Graphing and Solving Quadratic Inequalities Example 3 Solve 0 ≤ -2x 2 – 6x + 1 by graphing

8. 5.8 – Graphing and Solving Quadratic Inequalities Example 4 The height of a ball above the ground after it is thrown upwards at 40 feet per second can be modeled by the function h(x) = 40x – 16x 2, where the height h(x) is given in feet and the time x is in seconds. At what time in its flight is the ball within 15 feet of the ground?

9. 5.8 – Graphing and Solving Quadratic Inequalities Example 5 Solve x 2 + x ≤ 2 algebraically

10. 5.8 – Graphing and Solving Quadratic Inequalities HOMEWORK Page 298 #11 – 26