Quadratic Formula Calculator

x = (−b ± √(b² − 4ac)) / 2a solves every quadratic. The discriminant b² − 4ac decides the character before you solve: positive means two real roots, zero one repeated root, negative a complex pair — the parabola misses the x-axis entirely.

Quadratics model anything with squared terms: projectile flight (when does it land → roots), profit curves (break-even points), and areas. The vertex, also shown, is the max or min — the peak of the throw, the profit-maximizing price.