Vertex Calculator
Find the vertex of a quadratic function y = ax² + bx + c. Enter coefficients a, b, and c to get the vertex coordinates (h, k) and the axis of symmetry.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Vertex Calculator
This calculator finds the vertex of a quadratic function in the form f(x) = ax² + bx + c.
- Enter coefficient a (must be non-zero, e.g., 1, -2.5).
- Enter coefficient b (e.g., -3, 0).
- Enter coefficient c (e.g., 2, 4.1).
- Click "Calculate Vertex".
Results shown:
- Vertex coordinates (h, k) — the turning point of the parabola.
- Axis of symmetry — the vertical line x = h.
Note: All inputs accept decimal numbers. Coefficient a cannot be zero. Values are rounded to 4 decimal places for clarity.
Previous Results
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Frequently Asked Questions
The vertex is the highest or lowest point of a parabola, depending on whether it opens upward or downward. It is given by (h, k) where h = -b/(2a) and k = c - b²/(4a).
The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two mirror images. Its equation is x = h.
If a = 0, the equation is not quadratic but linear. The calculator will show an error because a must be non-zero for a parabola.
