How it works
The vertex is the point (h, k) on the axis x = h. For y = x² − 6x + 5, h = 3 and k = −4. Positive a gives a minimum; negative a gives a maximum. This calculation finds the turning point rather than the roots where the parabola meets y = 0.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Coefficient a | 1 | Enter a numeric value. |
| Coefficient b | -6 | Enter a numeric value. |
| Constant c | 5 | Enter a numeric value. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Coefficient a
- 1
- Coefficient b
- -6
- Constant c
- 5
Complete example results
- Vertex x-coordinate h
- 3
- Vertex y-coordinate k
- -4
Reading the result
Use quantities on the same basis. The starting value in percentage change, the denominator in a ratio and the length unit in geometry determine the meaning of the answer. Check the formula conditions alongside the example.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
Why is a = 0 rejected?
With a = 0 the expression is linear or constant and is not a parabola with one quadratic turning point.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.