Discriminant Calculator

Calculate discriminant, roots, vertex form, graph, and nature of quadratic roots — with full steps.

How It Works

  1. Enter coefficients. Type a, b, and c for ax² + bx + c = 0 in the main card.
  2. Get the discriminant. The tool computes Δ = b² − 4ac and labels the root type instantly.
  3. Read root nature. Δ > 0 = two real roots, Δ = 0 = one repeated root, Δ < 0 = complex roots.
  4. Full analysis. Use the advanced block for vertex form, intercepts, domain, range, and a parabola graph.
  5. Try examples. Click sample equations to load common classroom problems with step-by-step work.

Also try our Power Series Calculator or Simplify Calculator.

Enter values to see results.

Formula & Reference

Δ = b² − 4ac · x = (−b ± √Δ)/2a · Vertex: (−b/2a, f(−b/2a))