📐 Quadratic Equation Solver

Solve quadratic equations with detailed step-by-step solutions

📝 Standard Form: ax² + bx + c = 0

ax² + bx + c = 0
Enter the coefficients below

🎯 Solutions

📊 Discriminant Analysis

📝 Step-by-Step Solution

📈 Additional Information

💡 Understanding Quadratic Equations

  • Discriminant (Δ): b² - 4ac determines the nature of roots
  • Δ > 0: Two distinct real roots
  • Δ = 0: One repeated real root
  • Δ < 0: Two complex conjugate roots

🎯 Vertex Form: a(x - h)² + k = 0

a(x - h)² + k = 0
Enter the vertex form parameters

🎯 Solutions

🔄 Standard Form Conversion

📍 Vertex Information

💡 Vertex Form Benefits

  • Directly shows the vertex (h, k) of the parabola
  • Easy to identify the axis of symmetry: x = h
  • Helps determine if parabola opens upward (a > 0) or downward (a < 0)

✂️ Factored Form: a(x - r₁)(x - r₂) = 0

a(x - r₁)(x - r₂) = 0
Enter the roots and leading coefficient

📋 Standard Form

🎯 Roots Analysis

📊 Key Properties

💡 Factored Form Advantages

  • Roots (x-intercepts) are immediately visible
  • Easy to evaluate the function at specific points
  • Useful for graphing and understanding the parabola's behavior