Quadratic formula calculator

Solve ax² + bx + c = 0: real or complex roots, the discriminant, the vertex and a graph.

Your equation:

Graph

How it’s worked out

Discriminant
Δ = b² − 4ac
Quadratic formula
x = (−b ± √Δ) ÷ 2a
Roots

Questions people ask

What is the quadratic formula?

For ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the square root, b² − 4ac, is the discriminant.

What does the discriminant tell me?

Positive: two real roots. Zero: one repeated root (the parabola touches the x-axis). Negative: no real roots, two complex ones.