Finite real coefficients with a not equal to zero.
Completing The Square Calculator
Enter your values below to get the result first, then scroll for the full explanation and guidance.
Completed-square form
1(x + 3)^2 - 4a(x - h)^2 + k
Completed-square form: 1(x + 3)^2 - 4 (a(x - h)^2 + k)
The vertex is found from h = -b/(2a), then k is the polynomial value at h.
Quadratic vertex form
The vertex is found from h = -b/(2a), then k is the polynomial value at h.
Result snapshot
A quick visual read of the values behind this result.
This calculator updates instantly as your values change, so you can compare outcomes without extra steps.
Recommended next checks
- →The turning point is (h, k).
- Vertex
- (-3, -4)
Try different values to compare results.
Rewrite ax² + bx + c in completed-square form and identify its vertex.
Completed-square form
1(x + 3)^2 - 4a(x - h)^2 + k
Completed-square form: 1(x + 3)^2 - 4 (a(x - h)^2 + k)
The vertex is found from h = -b/(2a), then k is the polynomial value at h.
Quadratic vertex form
The vertex is found from h = -b/(2a), then k is the polynomial value at h.
Result snapshot
A quick visual read of the values behind this result.
This calculator updates instantly as your values change, so you can compare outcomes without extra steps.
Recommended next checks
- →The turning point is (h, k).
- Vertex
- (-3, -4)
Try different values to compare results.
Table of Contents
Table of Contents
About Completing The Square Calculator
Completing The Square Calculator helps you work through the main numbers for this topic quickly with a simple input flow and an instant result.
Use the calculator result as a practical starting point, then review the explanation and assumptions on the page if you want more context.
Calculation method
h = -b/(2a), k = c - b²/(4a), giving a(x-h)²+k.
Formula explained
Calculation flow
This calculator is structured for fast UK-focused estimates with clear inputs, repeatable logic, and instant results.
Formula
Input values -> calculation engine -> instant result
How the result is built
1Enter the values requested in the form.
2The calculator applies the configured formula logic.
3The result updates instantly with a breakdown.
4Use the output to compare scenarios quickly.
Example
Example verified by the calculator's polynomial algebra reference cases.
Assumptions
- Finite real coefficients with a not equal to zero.
Source basis
- UK-focused calculator flow
- Structured input validation
- Instant result breakdowns
FAQ
Common questions
Trust and notes
Assumptions and important notes
This calculator is designed to give a fast estimate using the method shown on the page. Results are most useful when your inputs are accurate and the tool matches your situation.
Use the result as guidance rather than a final diagnosis or professional decision. If the result could affect health, legal, financial, or compliance decisions, verify it with a qualified source where appropriate.
- Finite real coefficients with a not equal to zero.
Method
UK calculator guidance
Last reviewed
April 17, 2026