Completing the Square Worksheet

Grade 12 Math worksheet focusing on completing the square to solve quadratic equations and rewrite quadratic expressions into vertex form.

Grade 12 Math AlgebraCompleting the Square

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.SSE.B.3.BCCSS.MATH.CONTENT.HSA.APR.B.3

Topics

AlgebraCompleting the SquareQuadratic EquationsVertex Form

7 sections · Free to use · Printable

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Completing the Square

Name:

Date:

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Read each question carefully and show all your work. Use the method of completing the square to solve the equations or rewrite the expressions.

1. Solve the quadratic equation by completing the square: x² + 6x + 5 = 0

2. Solve the quadratic equation by completing the square: x² - 10x + 21 = 0

Rewrite the following quadratic expressions in vertex form y = a(x - h)² + k by completing the square.

3. y = x² + 4x + 7

y =

4. y = x² - 8x + 12

y =

5. Solve the quadratic equation by completing the square: 2x² + 12x + 10 = 0

6. Solve the quadratic equation by completing the square: 3x² - 18x + 15 = 0

7. Which of the following is the vertex form of y = x² + 2x - 3?

y = (x + 1)² - 4

y = (x - 1)² - 4

y = (x + 1)² + 2

y = (x - 1)² + 2

8. Completing the square can always be used to solve any quadratic equation.

True

False

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