Graphing Quadratic Inequalities

Quadratic Inequalities

Analyze inequalities of the form ax^2 + bx + c ? 0.

Last updated: June 2026 | By Patchworkr Team

Interactive Solver

x^2 +x +
0
Analysis
Discriminant:16
Roots:-2, 2
Opens:Upward
Solution Set
x > 2 or x < -2

What the discriminant tells you

Positive means two real roots, zero means one repeated root, and negative means no real roots.

Inequality pattern

Upward parabolas use the outside intervals for greater-than inequalities and the inside interval for less-than inequalities.

Worked Example

Solve x^2 - 4 > 0.

1. a = 1, b = 0, c = -4

2. Roots are -2 and 2

3. Positive outside the roots

Final answer: x < -2 or x > 2

Frequently Asked Questions

Can a be zero?

No. Then the expression is not quadratic.

What if the discriminant is negative?

There are no real roots.

Why use operator buttons?

So you can quickly switch between the four standard inequality forms.

Does the tool show exact intervals?

It gives readable interval-style solution text.

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