Quadratic Inequalities

Quadratic Inequalities

Quadratic inequalities can be solved graphically or algebraically.

Solve Graphically:

The graph of an inequality is the collection of all solutions of the inequality.

Example 1 (one variable inequality):

The trick to solving a quadratic inequality is to replace the inequality symbol with an equal sign and solve the resulting equation. The solutions to the equation will allow you to establish intervals that will let you solve the inequality.

Plot the solutions on a number line creating the intervals for investigation. Pick a number from each interval and test it in the original inequality. If the result is true, that interval is a solution to the inequality.

Example 2 (two variable inequality):

Test a point above the parabola and a point below the parabola into the original inequality. Shade the entire region where the test point yields a true result.

Solve Algebraically:

Solving quadratic inequalities algebraically can be somewhat of a challenge. Be careful to consider all of your options.

When you solved quadratic equations, you created factors whose product was zero, implying either one or both of the factors must be equal to zero.