What does the discriminant (b² - 4ac) tell you?

Quadratic Formula Calculator - Solve ax² + bx + c = 0 with Vertex

Solve quadratic equations with step-by-step discriminant analysis (Δ = b² - 4ac), real vs complex roots, and parabola vertex coordinates.

⚙️ Configuration & Inputs

Coefficient a Cannot be zero (quadratic term x²)

Coefficient b Linear term x

Constant c Constant y-intercept

📊 Results & Analysis

Solutions (Roots x₁, x₂) x₁ = 3, x₂ = 2 Factored: (x - 3)(x - 2) = 0

Discriminant (Δ = b² - 4ac) 1.00 Two Distinct Real Roots (Δ > 0)

Parabola Vertex (h, k) (2.50, -0.25) Minimum point (Opens Upward)

Axis of Symmetry x = 2.50 Vertical line of symmetry

The Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a)

Frequently Asked Questions

If Δ > 0, there are two distinct real roots. If Δ = 0, there is exactly one repeated real root (parabola touches the x-axis). If Δ < 0, there are two complex conjugate roots.