See the whole quadratic, not just the roots.

Enter ax² + bx + c = 0 and get exact or complex roots, discriminant, vertex, axis of symmetry, factorization, intercepts, graph, and a transparent step-by-step derivation.

Exact radicalsComplex rootsInteractive graphStep-by-step

Enter coefficients

Use any real numbers. The leading coefficient a must not be zero.

x² − 5x + 6 = 0

x₁3

x₂2

Discriminant1

Vertex(2.5, −0.25)

Axisx = 2.5

OpensUpward

Graph auto-scales around the vertex and roots. Axes and intercepts are shown when they fall inside the viewport.

Factor / root form

y-intercept

Vertex form

Nature of roots