+ 6-7 graphing and solving quadratic inequalities objectives: the student will be able to. 1) graph...

+6-7 Graphing and Solving Quadratic Inequalities

Objectives: The student will be able to….

1) graph Quadratic Inequalities in Two Variables.

2) solve Quadratic Inequalities in One Variable.

+Recall how to Graph Linear Inequalities:

+Graphing Quadratic Inequalities

You can graph quadratic inequalities in two variables using the same techniques you used to graph linear inequalities in two variables.

Steps:1) Determine whether the boundary should be

solid or dashed. Graph the quadratic function.

+2) Test a point inside the parabola. Substitute the ordered pair of your choice (x, y) into the original inequality to see if this ordered pair is a solution.

If the resulting inequality is TRUE, shade INSIDE the parabola.

If the resulting inequality is FALSE, shade OUTSIDE your parabola.

+Example 1: Graph a Quadratic Inequality

Recall: What different methods can we use to graph?

+Example 2: Graph a Quadratic Inequality

+Example 3: Graph a Quadratic Inequality

+Solving Quadratic Inequalities To solve a quadratic inequality in one variable, we need to analyze

the graph of the related quadratic function.

+Steps to Solving Quadratic Inequalities: Always start by graphing

If the original inequality was of the form Identify the x values for which the graph lies BELOW the x-axis.

If the original inequality was of the form Identify the x values for which the graph lies ABOVE the x-axis.

For < or > , include the x-intercepts in the solution.

+

Solve

Example 4: Solve by Graphing.

+Example 5: Solve by Graphing.

Solve

+

Solve

Example 6: Solve by Graphing.

+

Solve

Example 7: Solve by Graphing.

+Scavenger Hunt! Choose a partner.

Find a graph of a quadratic inequality around the room. Start with the problem on the bottom of the paper. You may

use your calculator to help you graph. Interpret whether you are solving or graphing the inequality. Each partner must write down the problem on their own sheet

of paper. Work together to graph/solve the given inequality. Search around the room for a graph/solution that matches

yours! Once you find it, move on to the next problem (located below

the graph/solution you just found).