Quadratic Equation Solver
Solve any quadratic equation of the form ax² + bx + c = 0. The calculator works out the discriminant to tell you how many real roots exist, then gives the roots, the vertex, the axis of symmetry and the factored form where it factorises neatly.
How It Works
The quadratic formula gives the roots as (−b ± √D) / 2a, where the discriminant D is b² − 4ac. The sign of D tells you what to expect before you even calculate: positive means two distinct real roots, zero means one repeated root, and negative means the parabola never crosses the x-axis, so the roots are a complex conjugate pair.
- Discriminant with an interpretation
- Two, one or no real roots — or complex roots
- Vertex and axis of symmetry
- x-intercepts, y-intercept and factored form
- Full step-by-step substitution
Reading the result
The roots are the x-values where the parabola crosses the axis. The vertex is its turning point, and whether it is a minimum or a maximum depends on the sign of a: positive a opens upwards, negative a opens downwards.
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