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Quadratic Equation Solver

Solve ax² + bx + c = 0 with real-time graphing and steps.

ax² + bx + c = 0
+
+
= 0
Value 'a' cannot be zero in a quadratic equation.
Solution Steps
Δ = b² - 4ac = ...
Root (x₁)
...
Root (x₂)
...
Vertex
...
Understanding Quadratics

The Quadratic Formula

The roots of any quadratic equation can be found using the standard formula:

x = (-b ± √(b² - 4ac)) / 2a

The term under the square root, b² - 4ac, is called the Discriminant (Δ).

The Discriminant (Δ)

The discriminant tells you what kind of roots to expect:

  • Δ > 0: Two real and distinct roots. The parabola crosses the x-axis twice.
  • Δ = 0: One real repeated root. The parabola touches the x-axis at its vertex.
  • Δ < 0: Two complex roots. The parabola does not touch the x-axis.