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mathClassic tool

Quadratic Formula Calculator

Find the discriminant, real or complex roots, vertex, and axis of symmetry for ax² + bx + c.

Use this quadratic formula calculator to solve equations in the form ax² + bx + c = 0 without reworking every step by hand. It computes the discriminant, classifies the roots and also shows the vertex of the related parabola.

Enter the coefficients a, b and c to get two real roots, one repeated root or a pair of complex roots when needed. That makes the tool useful for homework, algebra review, graph analysis, test prep and quick answer checks.

The output also includes the axis of symmetry and the quadratic expression used in the calculation, so you can double-check both the equation structure and the final interpretation.

This calculator solves quadratic equations and organizes the result into a quick, readable summary.

Quick note: in a quadratic function, coefficient a cannot be zero.

SummaryEnter coefficients a, b and c to solve the equation.
Equation—
Discriminant (Δ)—
Roots—
Classification—
Vertex—
Axis of symmetry—
Applied formulaΔ = b² - 4ac; x = (-b ± √Δ) / 2a

Use clear inputs to get a more useful result.