Math

Quadratic Equation Calculator

Solve ax² + bx + c = 0 for real roots.

Free to use — no sign-up or login.

Quadratic equation plot A Cartesian plot of the quadratic with its vertex, symmetry axis, intercept, and real roots when present.

Enter valid values to draw the figure.

a = x² coeff · b = x coeff · c = constant · V = vertex

Plot of y = ax² + bx + c showing the vertex, symmetry axis, intercept, and any real x-axis crossings.

Discriminant

Root 1

Root 2

This free Quadratic Equation Calculator covers Solve ax² + bx + c = 0 for real roots.

Roots come from the quadratic formula using the discriminant. Related math tools sit beside How it works, with no account required.

Using the Quadratic Equation Calculator

Solve ax² + bx + c = 0 for real roots. Typical inputs are a (x²), b (x) and c. How it works beside the form states the identity the Quadratic Equation Calculator applies.

FAQ

How do I use the Quadratic Equation Calculator?

Open the Quadratic Equation Calculator, fill a (x²), b (x) and c, and read the result. Enter a (x²), b (x), and c for the Quadratic Equation Calculator; use finite values in the indicated domain. The calculator reports Discriminant, Root 1, and Root 2: Roots come from the quadratic formula using the discriminant. Set a (x²) nonzero; a negative Discriminant has no real Root 1 or Root 2.

What formula does the Quadratic Equation Calculator use?

The Quadratic Equation Calculator uses the identity in How it works. In words: Enter a (x²), b (x), and c for the Quadratic Equation Calculator; use finite values in the indicated domain. The calculator reports Discriminant, Root 1, and Root 2: Roots come from the quadratic formula using the discriminant. Set a (x²) nonzero; a negative Discriminant has no real Root 1 or Root 2.