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Quadratic equation solver

modified2026-07-21statusfinished

Real/complex roots and vertex for ax² + bx + c = 0.

[7.2] Governing equation

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Vertex at $\left(-\frac{b}{2a},\ c-\frac{b^2}{4a}\right)$. Source: 1728 Software Systems.

vertex (h,k) x₁ x₂
FIG. 01 — parabola: roots x₁, x₂ and vertex (h, k)