Name

Date

Lesson
Practice A
1.7 For use with the lesson Complete the Square

Solve the equation by finding square roots.

1. x 2 1 2x 1 1 5 9 2. x 2 1 6x 1 9 5 1 3. x 2 2 4x 1 4 5 16

4. x 2 2 10x 1 25 5 4 5. x 2 2 14x 1 49 5 7 6. x 2 1 20x 1 100 5 12

1
7. x 2 2 x 1 }
45 1 8. 2x 2 1 16x 1 32 5 14 9. 4x 2 1 12x 1 9 5 16

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 4x 1 c 11. x 2 2 2x 1 c

12. x 2 1 18x 1 c 13. x 2 1 24x 1 c

14. x 2 2 14x 1 c 15. x 2 2 5x 1 c

16. x 2 1 x 1 c 17. x 2 1 7x 1 c

Solve the equation by completing the square.

18. x 2 2 2x 2 2 5 0 19. x 2 1 6x 1 3 5 0

20. x 2 1 8x 2 2 5 0 21. x 2 1 2x 1 5 5 0

22. x 2 1 10x 1 11 5 0 23. x 2 2 14x 1 10 5 0

24. x 2 2 x 1 1 5 0 25. x 2 2 x 2 3 5 0

Copyright Houghton Mifin Harcourt Publishing Company. All rights reserved.

Write the quadratic function in vertex form. Then identify the vertex.
26. y 5 x 2 1 8x 1 5 27. y 5 x 2 2 12x 1 1

28. y 5 x 2 1 4x 1 12 29. y 5 x 2 2 10x 1 3

Find the value of x.

30. Area of rectangle 5 40 31. Area of rectangle 5 78

x x

x17
x13
Lesson 1.7

32. Area of triangle 5 16 33. Area of triangle 5 40

x
x
x14

x22

Algebra 2
1-78 Chapter Resource Book
 Lesson 1.6 Perform Operations 5. False. If the complex number is real, the
with Complex Numbers, number equals its conjugate. 6. False. Sample
answer: The sum of two imaginary numbers can
continued
be a real number or an imaginary number. For
Practice Level C example, the sum of 4 1 2i and 3 2 2i is 7, which

answers
}
} 14 } is a real number.
1. 6i 3 2. 4 6 } 2 i 3. 26 6 i 10
} }
7. True. (a 1 bi)(a 2 bi) 5 a2 2 abi 1 abi 2 bi 2
} 22 25 5 a2 2 b2(21) 5 a2 1 b2, which is a real
4. 6i 6 5. 4 6 }
2 i 6. 22 6 } 5
i
number. 8. True. The absolute value of a 1 bi is
7. 8 2 4i 8. 1 2 11i 9. 27 2 8i 10. 25 2 10i }
a2 1 b2 and the absolute value of its conjugate
11. 30 12. 24 2 16i 13. 30i 14. 17 2 19i a 2 bi is
}
a2 1 (2b)2 5
}
a2 1 b2.
21 7
15. 221 1 6i 16. 4 1 2i 17. }2 }
10i 9. Sum of complex numbers: a 1 bi 1 c 1 di 5
10
(a 1 c) 1 (b 1 d)i; Complex conjugate of sum:
16 2 11 3 47 21
52 }
18. } 5i 19. }
172 }
17i 20. 2} 50
2 }
50i (a 1 c) 2 (b 1 d)i; Sum of complex conjugates:
a 2 bi 1 c 2 di 5 (a 1 c) 2 (b 1 d)i
1 1 54 80 }
21. }2 }
i 22. 2}1 } i 23. 61 10. Product of complex numbers: (a 1 bi) p
3 3 17 17
}
39 83
}
(c 1 di) 5 ac 1 adi 1 bci 1 bdi 2 5 (ac 2 bd) 1
3
24. } 25. }
3
26. a > 0, b > 0 (ad 1 bc)i; Complex conjugate of product:
27. a < 0, b > 0 28. a < 0, b < 0 (ac 2 bd) 2 (ad 1 bc)i; Product of complex
conjugates: (a 2 bi)(c 2 di) 5 ac 2 adi 2 bci 1
29. a > 0, b < 0 30. a < 0, b 5 0
bdi2 5 (ac 2 bd) 2 (ad 1 bc)i 11. h h0
31. a 5 0, b > 0 32. real 33. pure imaginary
34. real 35. imaginary Lesson 1.7 Complete the
Square
Study Guide
} }
1. 6i 2. 62i 3 3. 63i 2 4. 27 2 3i Teaching Guide
Copyright Houghton Mifin Harcourt Publishing Company. All rights reserved.

5. 6 2 11i 6. 28 2 24i 7. 22 1 26i 8. 85 1. x 2 1 6x 2 35 5 0 2. No; Sample answer:

3 i 1 3i The expression x2 1 6x 2 35 cannot be factored
9. }2 }
2 10. }51 }5 11. 1 1 3i
2 because there are no two integers whose sum is 6
1215. imag. and whose product is 235. No; Sample answer: if
5i
1 1 3i
you write x 2 5 26x 1 35 and take square roots,
you end up with x in the square root expression.
i
3. The expression is equivalent to the expression
2
1 real x 1 6x 2 35. 4. 3.63 ft 5. Sample answer: A
22i 22i
quadratic equation in the form
a1x 1 }
22 1 k 5 0, or a1x 1 }
b 2 b 2
} } 22 5 2k, can be
12. 2 13. 5 14. 10 15. 5
solved using the square root method (provided
Math and History Application 2k 0, otherwise there is no solution.) If you can
1. (3i, 3i 1 7); (3i 1 7, 3i 1 14); write any quadratic equation in this form, you will
(3i 1 14, 3i 1 21) 2. (1 1 i, 2i); (2i, 24); be able to solve all quadratic equations.
(24, 16) 3. (2 2 i, 6 2 4i); (6 2 4i, 23 2 48i);
Practice Level A
(23 2 48i, 21772 2 2208i) 4. (i 1 4, 16i 1 29);
(16i 1 29, 1856i 1 1169) 1. 24, 2 2. 24, 22 3. 22, 6 4. 3, 7
} } 1 3
Challenge Practice 5. 7 6 7 6. 210 6 2 3 7. 2}, }
2 2
1. Sample answer: x 2 1 25 5 0 2. Sample } 7 1
answer: (x 1 3)2 1 8 5 0 3. 1 4. 21 8. 24 6 7 9. 2}2, }2 10. 4; (x 1 2)2

Algebra 2
Chapter Resource Book A11
 }
3 7 }
Lesson 1.7 Complete the 11. 22 12. 2}6 }
2
2 i 13. 4 6 7
Square, continued 5 3 7
}
109
14. 26, 1 15. 2 6 i 16. 6
} } } }
11. 1; (x 2 1)2 12. 81; (x 1 9)2 2 2 6 6
} }
13. 144; (x 1 12)2 14. 49; (x 2 7)2 17 1
65
17. 1 6 }
2
i 18. }
26 }
10

5 2 1 2
25
1 2
4; x 2 }
15. }
1
2 16. } 1
4; x 1 } 2
2 19. y 5 (x 1 6)2 2 30; (26, 230)
7 2 20. y 5 (x 2 2)2 1 11; (2, 11)
4; 1x 1 }
49
22
} }
17. } 18. 1 6
3 19. 23 6
6 3 2
}
20. 24 6 3 2 21. 21 6 2i 22. 25 6
14
} 1 2
21. y 5 22 x 2 }
3 3 3
2 1 } 1 2
2; }2, }2
1 2
22. y 5 241x 1 } 4; 12} 42
1 11
42 2 }
1 3
}
1
13
} 11
23. 7 6
}
39 24. }
26 }
2 i 25. }
26 }
2
4, }

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) 2 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
19 5. 24 6 2 3
}
32. 4 33. 10 6. 1 6 i 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)

1. 27, 21 2. 22, 8 3. 21, 13 4. 21, 7 9. y 5 2(x 1 3)2 2 5; (23, 25) 10. The vertex
is (10, 9000), so the number of units that
5 7 } 2 4 3 }

2 2
6. 2 6
5. 2}, } 3 8. 2}46
7 7. 2}3, } 3 maximizes R is 10.
}
2 5 Problem Solving Workshop:
10. 16; (x 1 4)2
9. 2}6 }
3 3 Using Alternative Methods
11. 121; (x 2 11)2 12. 64; (x 1 8)2 1. 14 ft 2. 0.9 sec 3. 2011 4. 3.7 yd
2 2
9
1 3
4; x 1 }
13. } 2 81
2 14. } 1 9
4; x 2 } 2
2 Challenge Practice

Copyright Houghton Mifin Harcourt Publishing Company. All rights reserved.

} } 1. True. If the solutions of a quadratic equation
15. 4; (3x 2 2)2 16. 22 6
5 17. 5 6 15
} } are rational numbers p and q, then the quadratic
18. 1 6
10 19. 23 6 i 20. 24 6 23 equation can be written as (x 2 p)(x 2 q) 5 0.
} } 5 b 2
21. 26 6
22 22. 12 6 3 7 23. 2}2
}
2. False. The quadratic equation x 2 }
2 5 d 1 2
1 11 has two distinct irrational number solutions when
26 }
24. } 2
i 25. 21, 3
d is positive and not a perfect square. 3. True.
26. y 5 (x 1 7)2 2 38; (27, 238) You can use the completing the square method to
27. y 5 (x 2 4)2 2 6; (4, 26) solve any quadratic equation. However, it is easier
to solve the equation 2x2 2 8 5 0 by finding
28. y 5 2(x 1 1)2 2 7; (21, 27)
square roots.
3
29. y 5 3 x 2 }1 2
45 3 45
2 2 1 }
4; } 1
2, } 2
4 4. x 5 5 6
25 2 c
}
; c > 25
}

30. 7 31. 8 32. 55.4 ft 3 9 9
5. x 5 2}6 c 1 }
64
; c < 2}
8 64
Practice Level C
} 6. distance between Mountain View and Capital
2 3 13 3 11 3 7
1. 2}, 2 2. 2}, }
3. }
5,2} 4. 2}6 }
5 City: about 382.5 mi; distance between Rapid City
3 2 2 15 10
} }
and Capital City: about 221.5 mi
5. 20.7 6
3 6. 23, 8 7. 24 6
17
} }
} 3 37 7 11
8. 8 6 2 11 9. }
26 }
2
10. 2}26 }
2
i

Algebra 2
A12 Chapter Resource Book