Name———————————————————————— Lesson
1.7
Date —————————————
Practice B
For use with the lesson “Complete the Square”
Solve the equation by finding square roots.
1. x 2 1 8x 1 16 5 9
2. x 2 2 6x 1 9 5 25
3. x 2 2 12x 1 36 5 49
4. 2x 2 2 12x 1 18 5 32
5. 4x 2 2 4x 1 1 5 36
6. 5x 2 2 20x 1 20 5 35
1
2
7. x 2 2 }
​ 3 ​ x 1 }
​ 9 ​5 1
3
9
8. x 2 1 }
​ 2 ​ x 1 }
​ 16  ​ 5 3
9. 9x 2 1 12x 1 4 5 5
Find the value of c that makes the expression a perfect square trinomial.
Then write the expression as a square of a binomial.
10. x 2 1 8x 1 c
11. x 2 2 22x 1 c
12. x 2 1 16x 1 c
13. x 2 1 3x 1 c
14. x 2 2 9x 1 c
15. 9x 2 2 12x 1 c
16. x 2 1 4x 5 1
17. x 2 2 10x 5 210
18. x 2 2 2x 2 9 5 0
19. x 2 1 6x 1 10 5 0
20. x 2 1 8x 1 4 5 0
21. 3x 2 1 36x 5 242
22. x 2 2 24x 1 81 5 0
23. 4x 2 1 20x 1 25 5 0
24. 3x 2 2 3x 1 9 5 0
25. 6x 2 2 12x 2 18 5 0
Write the quadratic function in vertex form. Then identify the vertex.
26. y 5 x 2 1 14x 1 11
27. y 5 x 2 2 8x 1 10
28. y 5 2x 2 1 4x 2 5
29. y 5 3x 2 2 9x 1 18
Find the value of x.
30. Area of rectangle 5 84
x
x15
31. Area of triangle 5 20
1
x
2
x12
32. Shot Put In a track and field event, a contestant had a throw in the shot put that can
be modeled by y 5 20.02x 2 1 x 1 6 where x is the shot put’s horizontal distance
(in feet) and y is the corresponding height (in feet). How long was the throw?
Round the answer to the nearest tenth.
Algebra 2
Chapter Resource Book
Lesson 1.7
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Solve the equation by completing the square.
1-79
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14. 26, 1 15. 2​   ​6 ​   ​ i 16. ​   ​6 ​     
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6
6
Lesson 1.7 Complete the
Square, continued
11. 1; (x 2 1)2 12. 81; (x 1 9)2
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5 2
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​ 2 ​  ​ 16. }
​ 4 ​; ​ x 1 }
​ 2 ​  ​
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19. y 5 (x 1 6)2 2 30; (26, 230)
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20. 24 6 3​Ï 2 ​  21. 21 6 2i 22. 25 6 Ï
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1  2
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11
22. y 5 24​1 x 1 }
​ 4 ​ 2​ 2 }
​ 4  ​; ​1 2}
​ 4 ​, }
​ 4  ​ 2​
26. y 5 (x 1 4)2 2 11; (24, 211)
23. 4 24. 10 25. 11 26. 2160 ft/sec
27. y 5 (x 2 6)2 2 35; (6, 235)
Study Guide
28. y 5 (x 1 2) 1 8; (22, 8)
1. 36; (x 1 6)2 2. 81; (x 2 9)2
29. y 5 (x 2 5)2 2 22; (5, 222) 30. 5 31. 6
3. 400; (x 2 20)2 4. 5 6 Ï
​ 19 ​ 
32. 4 33. 10
6. 1 6 i ​Ï 5 ​  7. y 5 (x 2 6)2 1 2; (6, 2)
Practice Level B
8. y 5 (x 2 7)2 1 1; (7, 1)
2
1. 27, 21 2. 22, 8 3. 21, 13 4. 21, 7
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3
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11. 121; (x 2 11)2 12. 64; (x 1 8)2
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15. 4; (3x 2 2)2 16. 22 6 Ï
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27. y 5 (x 2 4)2 2 6; (4, 26)
28. y 5 2(x 1 1)2 2 7; (21, 27)
2
3
45 3 45
29. y 5 3​ x 2 }
​ 2 ​  2​ 1 }
​ 4  ​; ​ }
​ 2 ​, }
​ 4  ​  ​
2
}
4. x 5 5 6 Ï
​ 25 2 c ​ 
; c > 25
}
30. 7 31. 8 32. 55.4 ft
Practice Level C
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Algebra 2
Chapter Resource Book
1. True. If the solutions of a quadratic equation
are rational numbers p and q, then the quadratic
equation can be written as (x 2 p)(x 2 q) 5 0.
has two distinct irrational number solutions when
d is positive and not a perfect square. 3. True.
You can use the completing the square method to
solve any quadratic equation. However, it is easier
to solve the equation 2x2 2 8 5 0 by finding
square roots.
26. y 5 (x 1 7)2 2 38; (27, 238)
}
is (10, 9000), so the number of units that
maximizes R is 10.
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9. y 5 2(x 1 3)2 2 5; (23, 25) 10. The vertex
b 2
2. False. The quadratic equation ​ x 2 }
​ 2 ​  ​ 5 d
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Challenge Practice
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5. 24 6 2​Ï 3 ​ 
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2
9
3
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​ 4  ​; ​ x 2 }
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Problem Solving Workshop:
Using Alternative Methods
2
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​     ​ 10. 16; (x 1 4)2
A12
20. y 5 (x 2 2)2 1 11; (2, 11)
3 2
3 3 3
21. y 5 22​ x 2 }
​ 2 ​  ​ 1 }
​ 2 ​; ​ ​ }2 ​, ​ }2 ​  ​
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3
9
9
5. x 5 2​ } ​6 ​ c 1 }
​ 64  ​ ​  
; c < 2​ }
  ​ 
8
64
6. distance between Mountain View and Capital
City: about 382.5 mi; distance between Rapid City
and Capital City: about 221.5 mi
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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13. 144; (x 1 12)2 14. 49; (x 2 7)2