Math · Algebra

Quadratic Formula Calculator

Solve ax² + bx + c = 0 with real or complex roots, plus the discriminant, vertex and axis of symmetry — with step-by-step work.

x² − 5x + 6 = 0
Solutions
Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a    Discriminant: D = b² − 4ac
Vertex: (−b/2a, f(−b/2a))    Axis of symmetry: x = −b/2a

Real & complex

D > 0 gives two real roots, D = 0 one, D < 0 a conjugate pair.

Discriminant

Know immediately how many roots to expect.

Vertex & axis

Parabola features computed automatically.

Step-by-step

Full substitution into the quadratic formula shown.

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