Quadratic Equation Solver

Solve quadratic equations of the form ax² + bx + c = 0. Get step-by-step solutions, discriminant analysis, and graph information.

a ≠ 0
Equation:
x² - 3x + 2 = 0

Solutions (Roots)

x₁ = 2.00
x₂ = 1.00

Discriminant

Δ = b² - 4ac = 1
Two distinct real roots

Vertex / Axis of Symmetry

Vertex: (1.50, -0.25)
Axis: x = 1.50

AI-Powered Step-by-Step Solution

Parabola Graph Analysis

Quadratic Formula

x = -b ± √(b² - 4ac)
────────
2a

Discriminant Analysis

  • Δ > 0: Two distinct real roots
  • Δ = 0: One real root (double root)
  • Δ < 0: Two complex roots

Key Features

  • Vertex: (-b/2a, f(-b/2a))
  • Axis of Symmetry: x = -b/2a
  • y-intercept: (0, c)
  • Opens up if a > 0, down if a < 0