Quadratic Equation Solver

Solve ax² + bx + c = 0. Shows discriminant, roots, vertex, axis of symmetry, and a visual graph.

Equation: ax² + bx + c = 0
Graph
💡 Definition

Quadratic Equations

  • A quadratic equation has the form ax² + bx + c = 0.
  • The quadratic formula x = (-b ± √(b²-4ac)) / 2a gives the solutions.
  • The discriminant (b²-4ac) determines the nature of roots.
📖 How to use

Step by Step

  • Enter values for a, b, and c
  • Solutions update in real-time
  • View the parabola graph on the right
  • Check discriminant, vertex, and axis of symmetry
🎯 Use cases

When to use

  • Algebra homework and study
  • Physics projectile calculations
  • Engineering design problems
  • Teaching quadratic concepts

Frequently Asked Questions

What if a = 0?
If a = 0, it's not quadratic but linear (bx + c = 0), giving one solution x = -c/b.
What are complex roots?
When the discriminant (b²-4ac) is negative, roots are complex numbers with imaginary parts. These are shown with the 'i' notation.