Graphing and solving quadratic inequalities Section 5.7

Quadratic inequalities in two variables

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.

Graph of a quadratic inequality

Some more graphs of quadratic inequalities

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.

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.

Solving a quadratic inequality by graphing (continued)

Solving a quadratic inequality by graphing (continued)

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

Solving a quadratic inequality algebraically (continued)

Solving a quadratic inequality algebraically (continued)

Solving a quadratic inequality algebraically (continued)

Solving a quadratic inequality algebraically (continued)