Completing the square calculator
Enter the quadratic's coefficients to get its completed-square form, handy for graphing and finding the maximum or minimum.
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How to use it
- Enter coefficient a, coefficient b and coefficient c.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
ax² + bx + c = a(x - h)² + k with h = -b / 2a and k = c - b² / 4a. If a > 0 the parabola opens up and k is a minimum; if a < 0 it opens down and k is a maximum.
Example
Inputs: Coefficient a = 2, Coefficient b = 8, Coefficient c = 3. Result: Vertex form: y = 2(x + 2)^2 - 5; h: -2; k: -5.
Limits and caveats
- h and k are shown as decimals, not fractions.
- a must be non-zero.
Questions about this tool
Why complete the square?
It shows the parabola's vertex directly and is how the quadratic formula is derived.
How do I read the vertex from the form?
In y = a(x - h)² + k the vertex is (h, k). Note that (x + 2) means h = -2.
Does it give the maximum or minimum?
Yes. k is the minimum when a is positive and the maximum when a is negative, reached at x = h.