Quadratic Equation Solver
Solve quadratic equations and visualize roots on a graph.
x² -5x +6 = 0
Coefficients — ax² + bx + c = 0
Quadratic coefficient
Linear coefficient
Constant term
1
Discriminant (?)
(2.5, -0.25)
Vertex
x = 2.5
Axis of Symmetry
2 Real Roots
x1
3
x2
2
Parabola
Quadratic Formula
x = (-b ± v(b²-4ac)) / 2a ? = b²-4ac = 1
AlgebraRootsParabolaDiscriminantEquation
Solve any quadratic equation ax² + bx + c = 0 — find real or complex roots, vertex, axis of symmetry, and visualize the parabola on a dynamic SVG chart.
Key Features
Real & Complex Roots
Handles all three discriminant cases: two real roots (Δ > 0), a double root (Δ = 0), and complex conjugate roots (Δ < 0).
Discriminant Display
Shows Δ = b² − 4ac so you can verify the nature of the roots at a glance.
Vertex & Axis of Symmetry
Computes the vertex (−b/2a, c − b²/4a) and axis of symmetry x = −b/2a.
SVG Parabola
Plots the parabola with the vertex in amber and real roots in red. The viewport auto-scales.
How to Use
- 1Enter the coefficients a, b, and c (decimals and negatives supported).
- 2The equation, discriminant, roots, and parabola update instantly.
- 3Copy any root value with the copy button.