Quadratic Equation Calculator
Solve the quadratic equation ax² + bx + c = 0 instantly. Supports fractional inputs. View real or complex roots, the discriminant, vertex, and a visual parabola chart.
Equation Coefficients
Fractional values such as 3/4 or -1/2 can be used.
Equation Roots
One Real Root (Double Root)
Root 1 (x₁)
-0.50
Coefficient Weights
Parabola Graph
Coordinates Table
| X Coordinate | Y = f(x) |
|---|---|
| -5.50 | 25.00 |
| -4.50 | 16.00 |
| -3.50 | 9.00 |
| -2.50 | 4.00 |
| -1.50 | 1.00 |
| -0.50 (Vertex) | 0.00 |
| 0.50 | 1.00 |
| 1.50 | 4.00 |
| 2.50 | 9.00 |
| 3.50 | 16.00 |
| 4.50 | 25.00 |
Complete Math Guide
Mastering the Quadratic Equation
Welcome to the most comprehensive and visually intuitive Quadratic Equation Calculator available online. The quadratic equation is one of the most famous and fundamental concepts in algebra. It is the mathematical bridge that connects simple linear relationships to the complex, curved geometry of the real world.
Whether you are a student calculating the roots of a polynomial for homework, an engineer plotting the trajectory of a projectile, or an economist trying to find the vertex of a profit-maximization curve, this calculator provides instant, precise answers. Not only does it compute the standard real roots, but it also effortlessly handles complex (imaginary) roots, calculates the exact vertex, and plots the resulting parabola on an interactive coordinate plane.
Frequently Asked