1. 6-7 Graphing and Solving Quadratic Inequalities
Objectives
Students will be able to
Graph quadratic inequalities in two variables
Solve quadratic inequalities in one variable

2. You can graph quadratic inequalities in two variables using the same techniques as graphing linear inequalities in two variables.
Steps
Graph the related quadratic equation; remember that < or > will indicate a dashed parabola
Pick a test point clearly in one region
If the test point is true, shade the region containing the test point; if the test point is false, shade the opposite region

3. Example 1: Graph each inequality. 1)

4. 2)

5. Try this. 3)

6. Quadratic inequalities in one variable can be solved two different ways: graphically or algebraically.
To solve graphically:
Graph

7. Example 2: Use the graph of its related function to write the solutions of each inequality. 1)

8. 2)

9. Try these. 3) 4)

10. To solve a quadratic inequality in one variable algebraically:
Solve the related quadratic equation.
Plot the solutions on a number line.
Pick an x value in each interval and test to see that it satisfies the original inequality. The solutions are the region(s) that contain a test point that successful satisfies the original inequality.

11. Example 3: Solve each inequality algebraically. 1)

12. 2)

13. Try these. 3) 4)