How do I know if the vertex is a min or max?

If a is positive, the parabola opens upward and the vertex is a minimum. If a is negative, it opens downward and the vertex is a maximum.

Can I use this to check my quadratic equation solutions?

Yes, the vertex x-value is exactly halfway between the two roots (if real roots exist), which is a handy way to sanity-check a quadratic equation solver's output.

Quadratic Vertex Calculator

Calculate the vertex coordinates of a parabola defined by ax² + bx + c. The vertex is the parabola's minimum point (if a > 0) or maximum point (if a < 0), useful for optimization and graphing problems.

Inputs

Results

Vertex x: 2
Vertex y: -1

Try an example

Formula

Vertex x = −b / (2a), Vertex y = a·x² + b·x + c at that x

Learn How This Works

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