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How to Calculate Completing the Square

Convert a quadratic to vertex form by completing the square.

The Formula

ax² + bx + c → a(x+h)² + k

The completing the square formula uses the mathematical relationship: ax² + bx + c → a(x+h)² + k. Each variable in the formula represents a measurable quantity that affects the final result.

Step-by-Step Method

  1. 1Identify all input values needed for the completing the square calculation.
  2. 2Substitute your known values into the formula: ax² + bx + c → a(x+h)² + k.
  3. 3Perform the arithmetic operations in the correct order (PEMDAS/BODMAS).
  4. 4Check that your result has the correct units and is within a reasonable range.
  5. 5Verify using the interactive Completing the Square to confirm your answer.

Related Topics

completing squarequadraticalgebra

Use the Interactive Calculator

Skip the manual math — get instant results with our free Completing the Square calculator.

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