Graph each equation.

46. y 2 − 8 x = 0 y squared , minus 8 x equals 0
47. y 2 − 8 y + 8 x = − 16 y squared , minus 8 y plus 8 x equals negative 16
48. 2 x 2 − y + 20 x = − 53 2 x squared , minus y plus 20 x equals negative 53
49. x 2 = 12 y x squared , equals 12 . y
50. y = 4 ( x − 3 ) 2 − 2 y equals 4 . open x minus 3 close squared . minus 2
51. ( y − 2 ) 2 = 4 ( x + 3 ) open y minus 2 close squared . equals 4 open x plus 3 close

Write an equation of a parabola with vertex at (1, 1) and the given information.

52. directrix y = − 1 2 y equals negative , 1 half
53. directrix x = 3 2 x equals , 3 halves
54. focus at (1,0)
55. Writing Explain how to find the distance from the focus to the directrix of the parabola x = 2 y 2 . x equals 2 , y squared , .

C Challenge

56. Reasoning Use the definition of a parabola to show that the parabola with vertex (h, k) and focus (h, k + c) has the equation ( x − h ) 2 = 4 c ( y − k ) . open x minus h close squared . equals 4 c open y minus k close .
57. 1. What part of a parabola is modeled by the function y = x ? y equals square root of x question mark
    2. State the domain and range for the function in part (a).
58. Proof If the radius and depth of a satellite dish are equal, prove that the radius is four times the focal length.

Standardized Test Prep

SAT/ACT

59. What is the equation of a parabola with vertex at the origin and focus at ( 0 , 5 2 ) ? open . 0 comma , 5 halves . close . question mark
    1. x = − 1 10 y 2 x equals negative , 1 tenth , y squared
    2. x = 1 10 y 2 x equals , 1 tenth , y squared
    3. x = − 1 10 x 2 x equals negative , 1 tenth , x squared
    4. y = 1 10 x 2 y equals , 1 tenth , x squared

60. Use the information in the graph to find the equation for the graph.

    

    6. y 2 + 6 x = 0 y squared , plus 6 x equals 0
    7. y 2 − 6 x = 0 y squared , minus 6 x equals 0
    8. x 2 + 6 y = 0 x squared , plus 6 y equals 0
    9. x 2 − 6 y = 0 x squared , minus 6 y equals 0
61. Which expression is NOT equivalent to ( 25 x 4 y ) 1 3 ? open . 25 , x to the fourth , y . close super 1 third end super . question mark
    1. x 25 x y 3 x . cube root of 25 x y end root ,
    2. 5 x x y 3 5 x , cube root of x y end root ,
    3. 25 x 4 y 3 cube root of 25 , x to the fourth , y end root ,
    4. 625 x 8 y 2 6 the sixth , root of 625 , x to the eighth , y squared end root ,

Extended Response

62. Use the properties of logarithms to write log 12 in four different ways. Name each property you use.

Mixed Review

See Lesson 10-1.

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range.

63. x 2 + y 2 = 64 x squared , plus , y squared , equals 64
64. x 2 + 9 y 2 = 9 x squared , plus 9 , y squared , equals 9
65. 4 x 2 − 9 y 2 = 36 4 x squared , minus , 9 y squared , equals 36

Get Ready! To prepare for Lesson 10-3, do Exercises 66–69.

See Lesson 4-6.

Complete the square.

66. x 2 − 2 x + □ x squared , minus 2 x plus white square
67. x 2 + 4 x + □ x squared , plus 4 x plus white square
68. x 2 + 10 x + □ x squared , plus 10 x plus white square
69. x 2 − 6 x + □ x squared , minus 6 x plus white square

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