Quadratic Equation Solver

Solve equations of the form ax² + bx + c = 0. Get exact and decimal solutions, discriminant, and vertex information. All calculations run directly in your browser.

Coefficients (ax² + bx + c = 0)

Coefficient a must be non-zero, otherwise the equation is not quadratic.

Solution details

Discriminant (b² − 4ac)

Roots (x-intercepts)

x = 1, x = 2

Vertex (x, y)

x = 1.5, y = -0.25

Axis of symmetry

x = 1.5

Opens

Upward (a > 0)

For D > 0, there are two distinct real roots. For D = 0, there is one repeated real root. For D < 0, roots are complex (no real x-intercepts).

Quadratic formula recap

Standard form: ax² + bx + c = 0, with a ≠ 0.
Discriminant: D = b² − 4ac.
Roots: x = (−b ± √D) / (2a).
Vertex: x = −b / (2a), y = f(x) = a·x² + b·x + c.
If a > 0, the parabola opens upward; if a < 0, it opens downward.

This tool is for quick checks and learning support. For exact symbolic manipulation beyond the quadratic formula, consider a full CAS (computer algebra system).

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