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

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

3. 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

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

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

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

7. 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.

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

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

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

11. 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.

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

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

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

15. 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?

16. Homework
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