Quadratic Vertex Form Calculator
Enter the a, b, and c coefficients of a quadratic equation (ax² + bx + c) to find its vertex.
Quadratic Vertex Form Calculator
Find the vertex, axis of symmetry, and direction of opening of a quadratic function.
This is a straightforward algebraic calculation; it requires a to be non-zero (otherwise the equation is not quadratic).
Every quadratic function ax² + bx + c graphs as a parabola with a single vertex — either its minimum point (if it opens upward) or maximum point (if it opens downward). This calculator finds that vertex directly from the standard-form coefficients.
Example
- With the default values shown above, this calculator returns: Vertex X-Coordinate ≈ 2.0000; Vertex Y-Coordinate ≈ -1.0000; Parabola Opens: Upward (a is positive) — vertex is a minimum.
Frequently Asked Questions
What is the vertex formula?
The vertex x-coordinate is -b/(2a); substituting that value back into the original equation gives the vertex y-coordinate.
How do I know if the vertex is a minimum or maximum?
If a is positive, the parabola opens upward and the vertex is the minimum point; if a is negative, it opens downward and the vertex is the maximum point.