Quadratic Calculator
Solve any quadratic equation in the form ax² + bx + c = 0. Find real or complex roots, discriminant, vertex, axis of symmetry, factor form, and see the parabola instantly.
Provide values for a, b, and c in ax² + bx + c = 0.
The value b² − 4ac determines the type of roots.
See exact equation details, roots, vertex, and parabola shape.
x = (3 ± √1) ÷ 2
If b² − 4ac is positive, there are two distinct real roots. If it equals zero, there is one repeated real root. If it is negative, the equation has two complex conjugate roots.
A quadratic equation is a second-degree polynomial equation. Its graph is a parabola that opens upward when a is positive and downward when a is negative.
What happens if a equals zero?
The equation is no longer quadratic. It becomes linear, so this calculator requires a non-zero value for a.
Can this calculator show complex roots?
Yes. When the discriminant is negative, the calculator displays both roots in a + bi form.
What is the vertex of a parabola?
The vertex is the highest or lowest point of the parabola. Its x-coordinate is −b ÷ 2a.
What does a repeated root mean?
A repeated root occurs when the discriminant equals zero. The parabola touches the x-axis at exactly one point.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
This calculator is intended for educational and general mathematical use. Results are numerical approximations and should be independently verified for critical work.
