Practice C - MathnMind

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