Quadratic Equation Solver (ax² + bx + c = 0)
About Quadratic Equation Solver
The Quadratic Equation Solver finds real and complex roots (x₁, x₂) for standard second-degree polynomials (ax² + bx + c = 0) with step-by-step discriminant calculation, vertex coordinates, and parabolic curve visualization.
How to Use Quadratic Equation Solver
Step 1
Enter the coefficients a, b, and c into the corresponding input fields (a ≠ 0).
Step 2
Inspect the calculated roots x₁ and x₂.
Step 3
Review discriminant classification and vertex coordinates.
Step 4
Copy the step-by-step solution steps for your notes.
Practical Use Cases for Quadratic Equation Solver
Algebra & Calculus Education
Solve polynomial homework problems and understand the quadratic formula derivation step-by-step.
Physics & Trajectory Modeling
Calculate projectile motion flight times, apex heights, and impact coordinates where acceleration follows a parabolic curve.
Input & Output Examples
Solving 2x² - 4x - 6 = 0
a = 2, b = -4, c = -6
Roots: x₁ = 3, x₂ = -1 | Discriminant (Δ): 64 (Two Real Roots) | Vertex: (1, -8)
Key Features & Performance
- ✓Solves any quadratic equation: ax² + bx + c = 0.
- ✓Step-by-step quadratic formula breakdown: x = (-b ± √(b² - 4ac)) / 2a.
- ✓Discriminant analysis: Two real roots (Δ > 0), one double root (Δ = 0), or complex roots (Δ < 0).
- ✓Calculates parabola Vertex coordinates (h, k) and Axis of Symmetry.
- ✓100% Client-Side computation.
- ✓1-Click Copy full step-by-step solution.
Key Terminology & Definitions
Discriminant (Δ = b² - 4ac)
The expression under the radical in the quadratic formula that reveals the nature and number of roots.
Parabola Vertex
The maximum or minimum turning point of a parabolic curve, given by the coordinates h = -b/(2a) and k = f(h).