Quadratic Equation Calculator

x = (-b ± √(b²-4ac)) / (2a). It solves any equation of the form ax² + bx + c = 0. The discriminant (b²-4ac) determines the nature of roots: positive = 2 real roots, zero = 1 repeated root, negative = 2 complex roots.

The vertex is the highest or lowest point of the parabola. Its x-coordinate is -b/(2a), and the y-coordinate is found by plugging x back into the equation. If a > 0, the vertex is a minimum; if a < 0, it's a maximum.