Completing the Square Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Algebra 1CCSS HSA.SSE.B.3bAnswer key includedPDF · Print

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Easy: x² + bx + c, even b

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Worksheet variations

Take half the coefficient of x and square it. Add and subtract that number so the first three terms make a perfect square, then tidy up the constant. When a isn't 1, factor it out of the x-terms first.

Easyx² + bx + c, even b MediumOdd b (fractions)Harda ≠ 1

How to solve it: a worked example

Complete the square to write each quadratic in vertex form, a(x − h)² + k.

Start
Half of the x-coefficient, squared
Add and subtract it
Write the perfect square
Answer

Common mistakes to watch for

Adding the square without subtracting it again, which changes the expression.
Using half of b without squaring it.
When a isn't 1, forgetting to multiply the subtracted square by a.

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