Quadratic Formula Calculator
Solve quadratic equations using the quadratic formula. Find roots, vertex, and analyze parabola properties with detailed step-by-step solutions.
Quadratic Equation: ax² + bx + c = 0
Enter the coefficients of your quadratic equation
x²
x
constant
The Quadratic Formula
x = (-b ± √(b² - 4ac)) / (2a)
For any quadratic equation ax² + bx + c = 0
Components:
- a, b, c are the coefficients of the quadratic equation
- b² - 4ac is called the discriminant (Δ)
- The ± symbol gives us two solutions (roots)
- a ≠ 0 (otherwise it's not a quadratic equation)
Why It Works:
The quadratic formula is derived by completing the square on the general quadratic equation. It works for any quadratic equation and always gives the correct roots, whether they're real or complex.