Quadratic Equation Solver

Solve quadratic equations (ax² + bx + c = 0). Find roots, discriminant, vertex, and axis of symmetry with a visual graph.

a (x² coefficient)

b (x coefficient)

c (constant)

Tab to move between fields

Root 1 (x₁)

Root 2 (x₂)2

Discriminant (b²-4ac)1

Vertex(2.5, -0.25)

Axis of Symmetry2.5

Nature of RootsTwo distinct real roots

How to Use This Calculator

Enter coefficients a, b, and c for the equation ax² + bx + c = 0 (a must be non-zero for a true quadratic).
The calculator evaluates the discriminant b² − 4ac to determine the nature of the roots.
If the discriminant > 0, two distinct real roots exist; if = 0, one repeated root; if < 0, two complex conjugate roots.
Roots are found using the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a.
The Vertex (−b/2a, f(−b/2a)) is the turning point of the parabola; it is the minimum if a > 0 and maximum if a < 0.
The parabola graph updates in real time so you can see how changing a, b, or c shifts and stretches the curve.

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Formula

x = (-b ± √(b² - 4ac)) / 2a

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