Parabola Vertex Calculator
Find the vertex of a parabola from standard form, vertex form, or three points. The calculator shows the axis of symmetry, roots, focus, directrix, and graph.
How to Find the Vertex of a Parabola
For a quadratic in standard form, the vertex is the turning point of the parabola. It gives the minimum point when the parabola opens upward and the maximum point when it opens downward.
h is the x-coordinate of the vertex for y = ax^2 + bx + c.
k is the y-coordinate of the vertex.
Supported Inputs
| Input | Fields | Use case |
|---|---|---|
| Standard form | a, b, c | most homework and algebra problems |
| Vertex form | a, h, k | when the vertex is already visible |
| Three points | three distinct x-values and y-values | when a parabola must be fitted from points |
What the Calculator Shows
- vertex coordinates and axis of symmetry
- whether the vertex is a minimum or maximum
- real roots when they exist
- focus, directrix, and focal distance
- a scaled graph for visual checking
Worked Example
For - 4x + 3, the vertex x-coordinate is 2 and the vertex y-coordinate is -1.
Substitute a = 1 and b = -4.
The vertex is (2, -1).
Frequently Asked Questions
Sources and References
Calculations are based on the listed reference sources. Links open in a new tab.
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