How do I use the Quadratic Equation Solver?

Enter coefficients a, b, and c for ax² + bx + c = 0. Click Solve to find the roots. View the discriminant, vertex, and axis of symmetry. See the step-by-step solution and interactive graph.

Is the Quadratic Equation Solver free?

Yes, the Quadratic Equation Solver is completely free. It runs entirely in your browser with no signup, no download, and no data sent to any server.

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Quadratic Equation Solver

Solve ax² + bx + c = 0. Get real or complex roots, discriminant, vertex, axis of symmetry, step-by-step solution, and graph.

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Quadratic Equation Solver

Solve ax² + bx + c = 0. Get real or complex roots, vertex, axis of symmetry, and a visual graph.

x² + x + = 0

How to use

How to Use the Quadratic Equation Solver

1 Enter coefficients a, b, and c for ax² + bx + c = 0.
2 Click Solve to find the roots.
3 View the discriminant, vertex, and axis of symmetry.
4 See the step-by-step solution and interactive graph.

The quadratic formula x = (-b ± √(b²-4ac)) / 2a solves any quadratic equation. The discriminant (Δ = b²-4ac) determines the nature of roots: Δ > 0 gives two real roots, Δ = 0 gives one repeated root, and Δ < 0 gives two complex conjugate roots.

The graph shows the parabola y = ax² + bx + c with roots marked in red and the vertex in green. The vertex (-b/2a, f(-b/2a)) is the minimum point when a > 0 or maximum when a < 0. The axis of symmetry is the vertical line x = -b/2a.

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