C Challenge

49. Construction A blueprint for a 15 ft-by-9 ft rectangular wall has a square window in the center. If each side of the window is x feet, the function y = 135 − x 2 y equals 135 minus , x squared  gives the area (in square feet) of the wall without the window.
    1. Graph the function.
    2. What is a reasonable domain for the function? Explain.
    3. What is the range of the function? Explain.
    4. Estimate the side length of the window if the area of the wall is 117  ft 2 . 117 , ft squared , .
50. Reasoning Complete each statement. Assume a ≠ 0 . eh not equal to 0 .
    1. The graph of y = a x 2 + c y equals , eh x squared , plus c  intersects the x-axis in two places when ?.
    2. The graph of y = a x 2 + c y equals , eh x squared , plus c  does not intersect the x-axis when ?.
51. Consider the graphs of y = a x 2 y equals , eh x squared  and y = ( a x ) 2 . y equals . open eh x close squared . .  Assume a ≠ 0 . eh not equal to 0 .
    1. For what values of a will both graphs lie in the same quadrant(s)?
    2. For what values of a will the graph of y = a x 2 y equals , eh x squared  be wider than the graph of y = ( a x ) 2 ? y equals . open eh x close squared . question mark

Standardized Test Prep

SAT/ACT

52. Which equation has a graph that is narrower than the graph of y = 4 x 2 + 5 ? y equals , 4 x squared , plus 5 question mark
    1. y = 4 x 2 − 5 y equals , 4 x squared , minus 5
    2. y = − 5 x 2 + 4 y equals negative , 5 x squared , plus 4
    3. y = 0 . 75 x 2 + 5 y equals 0 . , 75 x squared , plus 5
    4. y = − 0 . 75 x 2 − 4 y equals negative 0 . , 75 x squared , minus 4
53. Kristina is evaluating some formulas as part of a science experiment. One of the formulas involves the expression 24 − ( − 17 ) . 24 minus open negative 17 close .  What is the value of this expression?
    6. − 41 negative 41
    7. − 7 negative 7
    8. 7
    9. 41
54. Which expression is equivalent to 8 ( x + 9 ) ? 8 open x plus 9 close question mark
    1. x + 72 x plus 72
    2. 8 x + 72 8 x plus 72
    3. 8 x + 17 8 x plus 17
    4. 8 x + 9 8 x plus 9
55. What is the solution of the equation 2 ( x + 3 ) + 7 = − 11 ? 2 open x plus 3 close plus 7 equals negative 11 question mark
    6. − 12 negative 12
    7. − 1 negative 1
    8. 1
    9. 12

Short Response

56. A rectangular dog run has an area of x 2 − 22 x − 48 . x squared , minus 22 x minus 48 .  What are possible dimensions of the dog run? Use factoring. Explain how you found the dimensions.

Mixed Review

See Lesson 8-8.

Factor completely.

57. 30 r 3 + 51 r 2 + 9 r 30 r cubed , plus , 51 r squared , plus 9 r
58. 15 q 3 − 18 q 2 − 10 q + 12 15 q cubed , minus , 18 q squared , minus 10 q plus 12
59. 7 b 4 + 14 b 3 + b + 2 7 b to the fourth , plus , 14 b cubed , plus b plus 2

Get Ready! To prepare for Lesson 9-2, do Exercises 60–65.

See Lesson 1-6.

Evaluate the expression − b 2 a fraction negative b , over 2 eh end fraction  for the following values of a and b.

60. a = − 2 , b = 3 eh equals negative 2 comma b equals 3
61. a = − 5 , b = − 4 eh equals negative 5 comma b equals negative 4
62. a = 8 , b = 6 eh equals 8 comma b equals 6
63. a = 10 , b = − 7 eh equals 10 comma b equals negative 7
64. a = − 4 , b = 1 eh equals negative 4 comma b equals 1
65. a = − 12 , b = − 48 eh equals negative 12 comma b equals negative 48

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