6-7 Graphing and Solving Quadratic Inequalities

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Presentation transcript:

6-7 Graphing and Solving Quadratic Inequalities Objectives: 1) Graph Quadratic Inequalities in Two Variables. 2) Solve Quadratic Inequalities in One Variable.

Recall how to Graph Linear Inequalities: y < -3x + 5

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: Determine whether the boundary should be solid or dashed. Graph the quadratic function. Test a point inside the parabola. Check to see if this ordered pair is a solution to the inequality. If the resulting Inequality is TRUE, shade INSIDE the parabola. If the resulting inequality is FALSE, shade OUTSIDE your parabola

Example 1a: Graph a Quadratic Inequality Graph y < x2 -6x – 7 Methods to graph: Table of values. Find x-intercepts (zeros) and vertex.

Example 1b: Graph a Quadratic Inequality Graph y > x2 - 4

Example 1c: Graph a Quadratic Inequality Graph y > - x2 + 10x - 25

Solving Quadratic Inequalities To solve a quadratic inequality in one variable, you can use the graph of the related quadratic function. To solve ax2 + bx + c < 0, graph y = ax2 + bx + c. Identify the x values for which the graph lies BELOW the x-axis. To solve ax2 + bx + c > 0, graph y = ax2 + bx + c. Identify the x values for which the graph lies ABOVE the x-axis. For < or >, include the x-intercepts in the solution.

Example 2a: Solve by Graphing. Solve x2 + 2x – 3 > 0

Example 2b: Solve by Graphing. Solve –x2 – 10x – 21 < 0

Example 2c: Solve by Graphing. Solve x2 – 9 > 0

Solve Quadratic Inequalities Algebraically Solve the related equation to identify the zeros. Plot the zeros on a number line (be careful with open vs. closed circles). Test a value in each interval to see if it satisfies the original inequality.

Example 3a: Solve Algebraically Solve x2 + x > 6

Example 3b: Solve Algebraically Solve x2 - 4x < 5

You Try It… Solve the quadratic inequality algebraically. 9x < 12x2

Application Vanessa has 180 feet of fencing that she intends to use to build a rectangular play area for her dog. She wants the play area to enclose at least 1800 square feet. What are the possible widths of the play area?

Homework Text p. 332-333 #s 1-8 all Text p. 333 #s 9-13 all