Quadratic Formula Calculator
Solve any quadratic equation ax² + bx + c = 0.
Finds real and complex roots, vertex, and discriminant.
Quadratic Solution
The Quadratic Formula solves any equation of the form ax² + bx + c = 0:
x = (-b ± √(b² - 4ac)) / 2a
The Discriminant (b² - 4ac) determines the nature of roots:
- Positive: Two distinct real roots
- Zero: One repeated real root
- Negative: Two complex (imaginary) roots
The Vertex of the parabola is at:
x = -b / 2a
y = f(-b / 2a)
The vertex is the maximum point if a < 0, or the minimum point if a > 0.