6 7 Graphing and Solving Quadratic Inequalities Objectives

6 -7 Graphing and Solving Quadratic Inequalities Objectives Students will be able to 1) Graph quadratic inequalities in two variables 2) Solve quadratic inequalities in one variable

• You can graph quadratic inequalities in two variables using the same techniques as graphing linear inequalities in two variables. Steps 1) Graph the related quadratic equation; remember that < or > will indicate a dashed parabola 2) Pick a test point clearly in one region 3) If the test point is true, shade the region containing the test point; if the test point is false, shade the opposite region

Example 1: Graph each inequality. 1)

2)

Try this. 3)

• Quadratic inequalities in one variable can be solved two different ways: graphically or algebraically. • To solve graphically: 1) Graph

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

2)

Try these. 3) 4)

• To solve a quadratic inequality in one variable algebraically: 1) Solve the related quadratic equation. 2) Plot the solutions on a number line. 3) 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.

Example 3: Solve each inequality algebraically. 1)

2)

Try these. 3) 4)