Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
The discriminant D = b² − 4ac determines the nature of roots:
- D > 0: Two distinct real roots
- D = 0: One repeated real root
- D < 0: Two complex (imaginary) roots
Vertex: (−b/2a, f(−b/2a)). Axis of symmetry: x = −b/2a.
FAQ
What are complex roots?
When the discriminant is negative, the square root produces imaginary numbers. The roots are expressed as a ± bi, where i = √−1.
What is the vertex of a parabola?
The vertex is the highest or lowest point of the parabola y = ax² + bx + c. If a > 0 the vertex is a minimum; if a < 0 it's a maximum.