1. Graphing and solving quadratic inequalities
Section 5.7

2. Quadratic inequalities in two variables

3. Graphing a quadratic inequality in two variables
Draw the parabola with equation
Make the parabola dashed for inequalities < or > and solid for inequalities with a
Choose a point (x, y) inside the parabola and check whether the point is a solution of the inequality.
If the point from the previous step is a solution, shade the region inside the parabola. If it is not a solution, shade the region outside the parabola.

4. Graph of a quadratic inequality

5. Some more graphs of quadratic inequalities

6. Quadratic inequalities in one variable
One way to solve a quadratic inequality in one variable is to use a graph.
To solve or
graph and indentify the x-values for which the graph lies below (or on and below) the x-axis.

7. Quadratic inequalities in one variable (continued)
To solve or
graph
and indentify the x-values for which the graph
lies above (or on and above) the x-axis.

8. Solving a quadratic inequality by graphing (continued)

9. Solving a quadratic inequality by graphing (continued)

10. Solving a quadratic inequality algebraically
Write the original inequality
Write the corresponding equation
Write the corresponding equation in standard form and solve it.
Plot the solutions to the corresponding equation on a number line, which will divide the number line into two or three intervals, providing the solutions are real
Pick a test value in each interval and see if it satisfies the inequality. If it does, all of the x-values in the interval will satisfy the inequality.
Put the solution in compound inequality format

11. Solving a quadratic inequality algebraically (continued)

12. Solving a quadratic inequality algebraically (continued)

13. Solving a quadratic inequality algebraically (continued)

14. Solving a quadratic inequality algebraically (continued)