+ 6-7 Graphing and Solving Quadratic Inequalities Objectives: The student will be able to…. 1) graph Quadratic Inequalities in Two Variables. 2) solve.

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Presentation transcript:

+ 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, include the x-intercepts in the solution.

+ Solve Example 4: Solve by Graphing.

+ Example 5: Solve by Graphing.  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).