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Completing the Square Worksheet

Grade 11 Algebra worksheet focusing on completing the square to solve quadratic equations and rewrite quadratic expressions.

Grade 11 Math AlgebraCompleting the Square
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Includes

Fill in the Blanks2 Short AnswerTrue / FalseMultiple ChoiceLong Answer

Standards

CCSS.MATH.CONTENT.HSA.SSE.B.3.BCCSS.MATH.CONTENT.HSA.REI.B.4.A

Topics

AlgebraQuadratic EquationsCompleting the SquareGrade 11Math
8 sections · Free to use · Printable
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Completing the Square

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Read each question carefully and follow the instructions to complete the square. Show all your work for full credit.

1. To complete the square for x² + bx, you add ( )² to the expression.

2. Completing the square transforms a quadratic expression into the form (x +  )² + k.

3. Rewrite the quadratic function f(x) = x² + 6x + 5 in vertex form by completing the square.

4. Rewrite the quadratic function g(x) = x² - 10x + 21 in vertex form by completing the square.

5. Completing the square can only be used to solve quadratic equations with a leading coefficient of 1.

T

True

F

False

6. The process of completing the square always results in real solutions for quadratic equations.

T

True

F

False

7. What constant term must be added to x² + 12x to complete the square?

a

6

b

12

c

36

d

144

8. Which of the following is equivalent to x² - 8x + 16?

a

(x + 4)²

b

(x - 4)²

c

(x - 8)²

d

(x + 8)²

9. Solve the equation x² + 4x - 12 = 0 by completing the square.

10. Solve the equation 2x² - 8x + 6 = 0 by completing the square.

11. The height h (in feet) of a projectile launched vertically upward from the ground with an initial velocity of 64 ft/s is given by h(t) = -16t² + 64t. Use completing the square to find the maximum height of the projectile and the time it takes to reach that height.