Quadratic Formula Solver
Solve ax² + bx + c = 0 equations
ax² + bx + c = 0
Results
Root 1
3
Root 2
-1
Vertex
(1, -8)
Step-by-Step Solution
Step-by-Step Solution:
ax² + bx + c = 0 → 2x² + (-4)x + (-6) = 0
Δ = b² - 4ac = (-4)² - 4(2)(-6) = 64
√Δ = 8
x₁ = (-b + √Δ) / 2a = (4 + 8) / 4 = 3
x₂ = (-b - √Δ) / 2a = (4 - 8) / 4 = -1
Vertex: (1, -8)
What is Quadratic Formula Solver?
Solve any quadratic equation using the quadratic formula. Enter coefficients a, b, and c to get both roots, the discriminant, vertex coordinates, and a visual graph of the parabola. Handles real and complex roots.
How to use
- Enter the coefficient values for a, b, and c in the equation ax² + bx + c = 0.
- View both roots (real or complex), the discriminant, and the vertex of the parabola.
- Copy the step-by-step solution or download the results for your homework or project.
Result
Solving 2x² - 4x - 6 = 0: enter a=2, b=-4, c=-6. The discriminant is 64 (positive, two real roots). Solutions: x = 3 and x = -1. Vertex at (1, -8).
Related Tools
Regression Calculator
Perform linear and polynomial regression analysis
Matrix Calculator
Perform matrix operations and calculations
Chi-Square Calculator
Perform chi-square statistical tests
Graphing Calculator
Plot mathematical functions on a graph
Area Calculator Map
Draw shapes on a map to calculate area
Z-Score Calculator
Calculate z-scores, percentiles, and probabilities