Quadratic Formula Calculator
Solve ax² + bx + c = 0 to find roots, discriminant, vertex, and axis of symmetry.
Solution
Step-by-Step:
About the Quadratic Formula Calculator
What is the Quadratic Formula?
The quadratic formula solves equations of the form ax² + bx + c = 0. It states that x = (-b ± �?b² - 4ac)) / 2a. The discriminant (b² - 4ac) determines the nature of the roots.
How to Use
Enter the coefficients a, b, and c, then click Calculate. The tool computes the discriminant, roots (real or complex), vertex, axis of symmetry, and opening direction.
What does the discriminant tell me?
If D > 0, there are two distinct real roots. If D = 0, one real root. If D < 0, two complex conjugate roots.
Can a be zero?
No. If a = 0, the equation is linear, not quadratic. The calculator will prompt you if a is zero or missing.
How is the vertex calculated?
The vertex x-coordinate is h = -b / 2a. The y-coordinate is k = f(h) = a·h² + b·h + c.
Is this calculator free?
Yes, BestCalc's quadratic formula calculator is completely free with no ads or registration required.