Quadratic Solver
Roots, discriminant and vertex for ax² + bx + c.
About Quadratic Solver
Quadratic Solver finds the roots of ax² + bx + c = 0, along with the discriminant, the vertex and the axis of symmetry. It handles complex roots rather than just reporting "no solution", which is what most school-level calculators do when the discriminant is negative.
How to use it
- Enter the coefficients a, b and c. a cannot be zero, or the equation is linear.
- Read the roots, the discriminant and the vertex.
- The vertex tells you the minimum or maximum of the parabola.
Questions
What does the discriminant tell me?
b² − 4ac. Positive means two distinct real roots, zero means one repeated root, negative means two complex roots. It tells you the shape of the answer before you calculate it.
What are complex roots?
Solutions involving i, the square root of −1. They mean the parabola never crosses the x-axis. They are still valid answers and matter in engineering and physics.
What is the vertex for?
It is the turning point — the minimum if a is positive, the maximum if negative. In applied problems that is usually the answer you actually want: peak height, minimum cost.
Quadratic Solver is free and runs entirely in your browser. No account, no upload, no watermark, no limit on use.