Practice C - MathnMind

Copyright © Holt McDougal. All rights reserved.
Name ——————————————————————— Date ————————————
LESSON
4.7
Practice C
For use with pages 268–275
Solve the equation by fi nding square roots.
1. x2 2 4
} x 1
3 4
} 5
9 16
}
9
2. 4x2 2 20x 1 25 5 64
3. 9x2 1 6
} x 1
5 1
}
25 5 4 4. 100x2 1 60x 1 9 5 28
5. x 2 1 1.4x 1 0.49 5 3 6. 0.04x 2 2 0.2x 1 0.25 5 1.21
Solve the equation by completing the square.
7. x 2 1 8x 2 1 5 0 8. x 2 2 16x 5 220
9. x 2 2 3x 2 7 5 0 10. x 2 1 7x 1 15 5 0
11. 2x 2 1 8x 1 4 5 x 2 1 4x 12. 3x 2 1 6x 5 2x 2 1 3x 2 4
13. 3x 2 2 24x 1 27 5 0 14. 2x 2 1 10x 1 1 5 13
15. 2x 2 1 10x 5 217 16. 3x 2 2 5x 2 8 5 2x 2 3
17. 3x 2 2 x 1 5 5 x 2 1 3x 2 14 18. 6x 2 2 5x 2 13 5 x 2 2 11
Write the quadratic function in vertex form. Then identify the vertex.
19. y 5 x 2 1 12x 1 6 20. y 5 x 2 2 4x 1 15
21. y 5 22x 2 1 6x 2 3 22. y 5 24x 2 2 2x 2 3
Find the value of x.
23. Area of parallelogram 5 60 24. Area of trapezoid 5 200
x 1 2
x 1 6
x
1
x 1 7
2
3x 2 2
25. Softball A recreational softball team paid a league entry fee of $825. The cost was
covered by equal contributions from each member on the team. If there were four
more team members, each person could contribute $20 less. How many members
does the team have?
26. Falling Object An object is propelled upward from the top of a 300 foot building.
The path that the object takes as it falls to the ground can be modeled by
y 5 216t 2 1 80t 1 300 where t is the time (in seconds) and y is the corresponding
height (in feet) of the object. The velocity of the object can be modeled by
v 5 232t 1 80 where t is time (in seconds) and v is the corresponding velocity
of the object. What is the velocity of the object when it hits the ground?
Algebra 2
Chapter 4 Resource Book
LESSON 4.7
251

ANSWERS
A48
Lesson 4.6, continued
Review for Mastery
1. 6i 2. 62i Ï }
3 3. 63i Ï }
2 4. 27 2 3i; real
part, 7 imaginary part
5. 6 2 11i real part, 6; imaginary part, 211i
6. 224i 2 8 7. 22 1 26i 8. 85
9. 3
} 2
2 i
} 10.
2 1
} 1
5 3i
} 11. 1 1 3i
5
12–15.
imag.
5i
Algebra 2
Chapter 4 Resource Book
i
22i
1
1 1 3i
real
2 2 i
12. 2 13. 5 14. Ï }
10 15. Ï }
5
Challenge Practice
1. Sample answer: x 2 1 25 5 0 2. Sample
answer: (x 1 3) 2 1 8 5 0 3. 1 4. 21
5. False. If the complex number is real, the
number equals its conjugate. 6. False. Sample
answer: The sum of two imaginary numbers can
be a real number or an imaginary number. For
example, the sum of 4 1 2i and 3 2 2i is 7, which
is a real number.
7. True. (a 1 bi)(a 2 bi) 5 a2 2 bi 1 bi 2 bi2 5 a2 2 b2 (21) 5 a2 1 b2 , which is a real
number. 8. True. The absolute value of a 1 bi is
Ï }
a2 1 b2 and the absolute value of its conjugate
a 2 bi is Ï }
a2 1 (2b) 2 5 Ï }
a2 1 b2 .
9. Sum of complex numbers: a 1 bi 1 c 1 di 5
(a 1 c) 1 (b 1 d)i; Complex conjugate of sum:
(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
10. Product of complex numbers: (a 1 bi) p
(c 1 di) 5 ac 1 adi 1 bci 1 bdi2 5 (ac 2 bd) 1
(ad 1 bc)i; Complex conjugate of product:
(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
bdi2 5 (ac 2 bd) 2 (ad 1 bc)i 11. h ≤ h0 Lesson 4.7
Practice Level A
1. 24, 2 2. 24, 22 3. 22, 6 4. 3, 7
5. 7 6 Ï }
7 6. 210 6 2 Ï }
3 7. 2 1
} ,
2 3
}
2
8. 24 6 Ï }
7 9. 2 7
} ,
2 1
} 10. 4; (x 1 2)
2 2
11. 1; (x 2 1) 2 12. 81; (x 1 9) 2
13. 144; (x 1 12) 2 14. 49; (x 2 7) 2
15. 25
}
4 ; 1 x 2 5
}
2 2 2
16. 1
} ;
4 1 x 1 1
}
2 2 2
17. 49
}
4 ; 1 x 1 7
}
2 2 2
18. 1 6 Ï }
3 19. 23 6 Ï }
6
20. 24 6 3 Ï }
2 21. 21 6 2i 22. 25 6 Ï }
14
23. 7 6 Ï }
39 24. 1
} 6
2 Ï} 3 1
} i 25. } 6
2 2 Ï} 13
}
2
26. y 5 (x 1 4) 2 2 11; (24, 211)
27. y 5 (x 2 6) 2 2 35; (6, 235)
28. y 5 (x 1 2) 2 1 8; (22, 8)
29. y 5 (x 2 5) 2 2 22; (5, 222) 30. 5 31. 6
32. 4 33. 10
Practice Level B
1. 27, 21 2. 22, 8 3. 21, 13 4. 21, 7
5. 2 5
} ,
2 7
} 6. 2 6 Ï
2 }
7 7. 2 2
} ,
3 4
} 8. 2
3 3
} 6 Ï
4 }
3
9. 2 2
} 6
3 Ï} 5
} 10. 16; (x 1 4)2
3
11. 121; (x 2 11) 2 12. 64; (x 1 8) 2
13. 9
} ;
4 1 x 1 3
}
2 2 2
14. 81
}
4 ; 1 x 2 9
}
2 2 2
15. 4; (3x 2 2) 2 16. 22 6 Ï }
5 17. 5 6 Ï }
15
18. 1 6 Ï }
10 19. 23 6 i 20. 24 6 2 Ï }
3
21. 26 6 Ï }
22 22. 12 6 3 Ï }
7 23. 2 5
}
2
24. 1
} 6
2 Ï} 11
} i 25. 21, 3
2
26. y 5 (x 1 7) 2 2 38; (27, 238)
27. y 5 (x 2 4) 2 2 6; (4, 26)
28. y 5 2(x 1 1) 2 2 7; (21, 27)
29. y 5 3 1 x 2 3
}
2 2 2 1 45
}
4 ; 1 3
} ,
2 45
}
4 2
30. 7 31. 8 32. 55.4 ft
Practice Level C
1. 2 2
} , 2 2. 2
3 3
} ,
2 13 3
} 3. 2 } ,
2 5 11 3 Ï} 7
} 4. 2 } 6 }
15 10 5
5. 20.7 6 Ï }
3 6. 23, 8 7. 24 6 Ï }
17
8. 8 6 2 Ï }
11 9. 3
} 6
2 Ï} 37 7
} 10. 2 } 6
2 2 Ï} 11
}
2 i
11. 22 12. 2 3
} 6
2 Ï} 7
} i 13. 4 6 Ï} 7
2
14. 26, 1 15. 2 5
} 6
2 3
} i 16.
2 7
} 6
6 Ï} 109
}
6
Copyright © Holt McDougal. All rights reserved.

Copyright © Holt McDougal. All rights reserved.
Lesson 4.7, continued
17. 1 6 Ï} 34 1
} i 18. } 6
2 2 Ï} 65
}
10
19. y 5 (x 1 6) 2 2 30; (26, 230)
20. y 5 (x 2 2) 2 1 9; (2, 9)
21. y 5 22 1 x 2 3
}
2 2 2
22. y 5 24 1 x 1 1
}
4 2 2
1 3
}
;
2 1 3
} ,
2 3
}
2 2
2 11
}
4 ; 1 2 1
} ,
4 11
}
4 2
23. 4 24. 10 25. 11 26. 2160 ft/sec
Review for Mastery
1. 36; (x 1 6) 2 2. 81; (x 2 9) 2
3. 400; (x 2 20) 2 4. 5 6 Ï }
19 5. 24 6 2 Ï }
3
6. 1 6 i Ï }
5 7. y 5 (x 2 6) 2 1 2; (6, 2)
8. y 5 (x 2 7) 2 1 1; (7, 1)
9. y 5 2(x 1 3) 2 2 5; (23, 25) 10. The vertex
is (10, 9000), so the number of units that
maximizes R is 10.
Problem Solving Workshop:
Using Alternative Methods
1. 14 ft 2. 0.9 sec 3. 2011 4. 3.7 yd
Challenge Practice
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.
2. False. The quadratic equation 1 x 2 b
}
2 2 2
5 d
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 fi nding
square roots.
4. x 5 5 6 Ï }
25 2 c ; c > 25
5. x 5 2 3
} 6
8 Ï }
c 1 9 9
} ; c < 2 }
64 64
6. distance between Mountain View and Capital
City: about 382.5 mi; distance between Rapid City
and Capital City: about 221.5 mi
Lesson 4.8
Practice Level A
1. 2x2 1 x 1 4; a 5 2, b 5 1, c 5 4
2. x2 2 2x 2 3; a 5 1, b 5 22, c 5 23
3. 24x2 2 3x 2 2; a 5 24, b 5 23, c 5 22
4. 22x2 1 6x 2 9; a 5 22, b 5 6, c 5 29
5. 27 6. 27 7. 0 8. 17 9. 16 10. 224
11. 12; two real 12. 0; one real
13. 216; two imaginary 14. 1; two real
15. never 16. never 17. always
18. 1, 2 19. 2 5
} 6
2 Ï} 17 3
} 20. } 6
2 2 Ï} 5
}
2
21. 1 6 Ï} 6
Ï} 2 2
} 22. 1 6 } 23. 2 } , 0
2 2 3
24. 9 Ï} 21 3
} 6 } 25. } 6
10 10 2 Ï} 15
}
2 i
26. 21, 5
} 27. 21, 2 28.
2 1
} , 21
2
29. 1 6 Ï }
3 30. 21, 2 31. 23, 22 32. 22, 4
33. 26, 21 34. 22, 3
} 35. 21,
2 1
} 36. 3.2
3
37. 4.5 38. 3.2 sec
Practice Level B
1. 211 2. 215 3. 49 4. 0 5. 21 6. 2124
7. 4; two real 8. 212; two imaginary
9. 0; one real 10. 16; two real
11. never 12. always
13. 22 6 Ï }
6 14. 5
} 6
4 Ï} 41
} 15. 0, 2
4
16. 1
} 6
4 Ï} 15 1
} i 17. } 18.
12 2 5
} 6
2 Ï} 7
}
2
19. 20.13, 1.25 20. 20.38, 1.47 21. 24, 6
22. 1 23. 3
} , 3 24. 2
2 5
} , 2
2 1
} 25. 2
3 1
} ,
2 2
}
5
26. 2 2
} ,
3 3
}
2
27. No. The area of the room is x(10 2 x) and can
be expressed as x(10 2 x) 5 28 which has no real
solutions. 28. h 5 216t2 1 64t 1 80 29. 2 sec
30. 144 ft 31. 5 sec
Practice Level C
1. 20; two real 2. 0; one real 3. 1; two real
4. 220; two imaginary 5. sometimes
6. sometimes 7. 2 5
} 6
2 Ï} 33
}
2
8. 3
} 6
4 Ï} 7
} i 9. 210 62 Ï} 29 10.
4 1
} 6
2 1
} i
2
11. 2 1
} , 3 12. 6 6 Ï
2 }
30 13. 2 1 Ï} 19
} 6 }
10 10 i
14. 0.44, 1.36 15. 20.34, 1.08 16. 0.62 6 0.41i
17. b 5 64 18. b 5 62 Ï }
15 19. no solution
20. c < 4
} 21. c <
3 25
1
} 22. c > 2 } 23. 45 mi/h
8 8
Algebra 2
Chapter 4 Resource Book
ANSWERS
A49