Completing the square calculator
Rewrite ax² + bx + c into vertex form a(x − h)² + k and show the steps of completing the square.
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Tool guide
Completing the square calculator: how it works
Practical information to understand the result and use this tool correctly.
About Completing the square calculator
Completing the square turns standard form into vertex form so the vertex and min/max are obvious.
Works for any a ≠ 0, including non-monic leading coefficients.
Used in graphing, optimization intros, and deriving the quadratic formula.
How to use it
- 1Enter a, b, and c.
- 2Read vertex form and (h, k).
- 3Confirm a ≠ 0.
Frequently asked questions
- What is (h, k)?
- The vertex of the parabola in vertex form a(x−h)²+k.
- Minimum or maximum?
- Minimum when a > 0, maximum when a < 0.