Quadratic Equation Solver
Enter the coefficients of a quadratic equation ax² + bx + c = 0. The solver reports the vertex and axis of symmetry, computes the discriminant Δ = b² − 4ac to classify the roots, and applies the quadratic formula x = (−b ± √Δ) / (2a), showing every substitution.
Formula and method
x = (−b ± √(b² − 4ac)) / (2a), discriminant Δ = b² − 4ac
First compute the discriminant Δ = b² − 4ac to classify the roots. If Δ > 0 there are two distinct real roots; Δ = 0 gives one repeated root x = −b/(2a); Δ < 0 yields a pair of complex conjugates x = −b/(2a) ± i·√(−Δ)/(2a). The vertex (−b/2a, c − b²/4a) and axis of symmetry are reported alongside.
Worked examples
Key terms
Frequently asked questions
What is the discriminant?
It is Δ = b² − 4ac. Positive gives two real roots, zero gives one repeated root, and negative gives complex conjugate roots.
Does it find the vertex?
Yes. The vertex is at (−b/2a, c − b²/4a), and the axis of symmetry is the vertical line through its x-coordinate.
Can it handle complex roots?
Yes. When the discriminant is negative the roots are returned in the form x = p ± qi.