Completing the Square Calculator
Rewrite a quadratic ax² + bx + c in vertex form a(x − h)² + k by completing the square, and read off the vertex and axis of symmetry.
Inputs explained
- Coefficient a (ax² + bx + c) — The coefficient of x². Cannot be zero.
- Coefficient b — The coefficient of x.
- Coefficient c — The constant term.
How to use it
- Fill in the fields above — each input has a hint describing exactly what to enter
- Press Calculate to get your result instantly, right on this page
- Copy the result, save the tool to favorites, or share and embed it anywhere
Understanding the result
Example: For x² + 6x + 5, the vertex form is (x + 3)² − 4, so the vertex is (−3, −4).
Frequently asked questions
How is the vertex form result related to the quadratic formula? Completing the square is actually the derivation behind the quadratic formula — the same (x+3)² − 4 form that gives the vertex here can also be solved for zero to find the equation's roots, arriving at the same solutions the quadratic formula would produce.
Why is the axis of symmetry always just the h-value from the vertex form? Because a parabola is symmetric around a vertical line through its vertex, the x-coordinate of the vertex (h) is by definition also the equation of the axis of symmetry — no separate calculation is needed.
Is the Completing the Square Calculator free to use? Yes — it is completely free, with no sign-up, no download and no usage limits. You can use it as often as you need.
Is my data private? Yes. The calculation runs entirely in your browser — the values you enter are never sent to our servers, stored or shared with anyone.
What information do I need? Just the following: Coefficient a (ax² + bx + c), Coefficient b, Coefficient c. Each field includes a hint explaining exactly what to enter.
Can I use it on my phone? Yes — the tool is fully responsive and works on any device, and the same calculator is available in the EasyWorkCalcs mobile app.
Privacy
Everything you enter into the Completing the Square Calculator is processed entirely in your browser. Nothing is uploaded, stored or shared — your data stays on your device.