Quadratic Formula Calculator - Solve ax² + bx + c = 0
Solve quadratic equations step-by-step using the quadratic formula. Calculate discriminant, find roots, determine vertex, and visualize the parabola graph.
Solution Results
Discriminant Analysis
Vertex Information
Understanding Quadratic Equations
The Quadratic Formula
For any quadratic equation ax² + bx + c = 0, the solutions are given by:
Where: a, b, c are coefficients and a ≠ 0
Discriminant (Δ = b² - 4ac)
- Δ > 0: Two distinct real roots
- Δ = 0: One repeated real root (perfect square)
- Δ < 0: No real roots (complex conjugate pair)
Vertex Formula
The vertex of the parabola y = ax² + bx + c is at:
The vertex represents the minimum (if a > 0) or maximum (if a < 0) point of the parabola.
How to Use the Quadratic Formula Calculator
Step 1: Enter Coefficients
Input the values for coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. Note that 'a' cannot be zero.
Step 2: Calculate
Click the solve button to calculate the discriminant, roots, and vertex using the quadratic formula.
Step 3: Review Steps
Examine the detailed step-by-step solution showing how the quadratic formula is applied to your equation.
Step 4: Visualize
View the parabola graph showing the roots, vertex, and axis of symmetry for better understanding.