Quadratic Equation Solver

How to use the quadratic equation solver

1. Fill in the fields — they start with a worked example.
2. Read the answer, and the arithmetic shown beneath it.
3. Copy the results, or adjust the inputs to compare scenarios.

About this tool

The roots come from the quadratic formula, and the discriminant b² − 4ac decides what kind of answer exists before you compute it: positive gives two real roots, zero gives one repeated root, and negative gives a complex pair.

The vertex is included because it answers the other common question — where the curve turns, and therefore its minimum or maximum value.

Common uses

• Solving a quadratic for homework, with the working.
• Finding where a parabola crosses the axis.
• Locating the maximum of a quadratic model.

Frequently asked questions

What does the discriminant tell me?

b² − 4ac. Positive means two real roots, zero means one, negative means the roots are complex and the curve never crosses the x-axis.

What if a is zero?

Then it is not quadratic but linear, and the tool solves bx + c = 0 instead.