by
Quadratic Equation Solver

Quadratic Equation Solver

Enter coefficients a, b, c for the equation ax² + bx + c = 0. Our calculator finds all roots, shows step-by-step solutions (Quadratic Formula, Completing the Square, Factoring when possible), and plots the parabola.

Parabola Visualization

Educational Notes

  • Quadratic Equation: Any equation of the form ax² + bx + c = 0, where a ≠ 0.
  • The Discriminant: D = b² - 4ac. It determines the type and number of real roots:
    • D > 0: Two distinct real roots
    • D = 0: One real repeated root
    • D < 0: Two complex (nonreal) roots
  • Graph Shape: The graph is a parabola. If a > 0, it opens upwards; if a < 0, it opens downwards.
  • Factoring: If the equation can be factored over real numbers, the roots are rational and factoring will show them directly.
  • Completing the Square: Rewriting the equation and isolating x by forming a perfect square trinomial.
  • Quadratic Formula: Universal formula to solve any quadratic: x = (-b ± √(b²-4ac)) / (2a)

Leave a Comment