Quadratic Equation Solver
Solve any quadratic equation ax² + bx + c = 0 to find its real or complex roots, plus the discriminant, vertex and axis of symmetry. Free and instant.
About Quadratic Equation Solver
The quadratic equation solver finds the roots of any equation in the form ax² + bx + c = 0. Enter the three coefficients and it returns the real or complex roots, the discriminant, the vertex of the parabola and its axis of symmetry.
It applies the quadratic formula, x = (−b ± √(b² − 4ac)) ÷ 2a, and classifies the result by the discriminant: positive gives two distinct real roots, zero gives one repeated root, and negative gives two complex conjugate roots — which the solver displays in full rather than reporting “no solution”.
Beyond homework checking, the vertex and axis of symmetry make it useful for graphing parabolas, optimization problems and physics questions like projectile motion, all free and instant in your browser.
How to use Quadratic Equation Solver
- Enter coefficient a — it cannot be zero for a true quadratic.
- Enter coefficients b and c, using negatives where the equation subtracts.
- Read the roots and the nature of the roots — two real, one repeated, or complex conjugates.
- Check the discriminant (b² − 4ac), the vertex (x, y) and the axis of symmetry for graphing.