# Quadratic Inequalities

This applet investigates how to find the solution set of a quadratic inequality and to interpret it on a graph of the related quadratic function.

###### Author and programmer: Ron Barrow

UK Years 12-13, KS5, KS4, Core 1 (C1) GCE Mathematics, Algebra and Functions

US - Grades 11 - 12

Instructions below
See also:
Quadratics: Completing the Square
Quadratics:The Discriminant

Quadratic Inverses
Simple Inequalities
Inequalities - Regions of Graphs

## How to Use this Applet

The applet on this page is designed to help you see what is meant by a quadratic inequality, and how to represent them on a graph of the related quadratic function. The standard quadratic expression is: a`x`² + b`x` + c. Varying a, b, c changes the curves. You can choose the inequality type from the drop-down menu at the top. As the curve changes, notice how the solution set and the highlighted section of the x-axis change. On the right you can see the inequality at the top and the solution set at the bottom.
You can also see the discriminant of the quadratic function and the zeroes if there are any. Calculating a quadratic inequality starts with solving the related equation and using these solutions to describe the inequality. If you wish to go back to the starting position, press the "Reset" button. Study this applet carefully and you will soon be familiar with this very important mathematical technique, which has many applications.