C Challenge

54. Copy and complete the table, which shows the first and second differences in y-values for consecutive x-values for a polynomial function of degree 2.

    x	y	1 st  diff. 1 super st end super . diff.	2 st  diff. 2 super st end super . diff.
    − 3 negative 3	14	− 8 negative 8	2
    − 2 negative 2	6	□ white square	2
    − 1 negative 1	□ white square	− 4 negative 4	2
    0	− 4 negative 4	− 2 negative 2	2
    1	□ white square	0	2
    2	− 6 negative 6	□ white square
    3	□ white square

55. The outputs for a certain function are 1, 2, 4, 8, 16, 32, and so on.

    1. Find the first differences of this function.
    2. Find the second differences of this function.
    3. Find the tenth difference of this function.
    4. Can you find a polynomial function that matches the original outputs? Explain your reasoning.
56. Reasoning A cubic polynomial function f has leading coefficient 2 and constant term 7. If f ( 1 ) = 7 f open 1 close equals 7  and f ( 2 ) = 9 , f open 2 close equals 9 comma  what is f ( − 2 ) ? f open negative 2 close question mark  Explain how you found your answer.

Standardized Test Prep

SAT/ACT

57. Which expression is a cubic polynomial?

    1. x 3 x cubed
    2. 3 x + 3 3 x plus 3
    3. 2 x 2 + 3 x − 1 2 x squared , plus 3 x minus 1
    4. 3 x 3 x

58. Which equation has − 3 ± 5 i negative 3 plus minus 5 i  as its solutions?

    6. x 2 + 6 x = − 34 x squared , plus 6 x equals negative 34
    7. x 2 + 6 x = − 14 x squared , plus 6 x equals negative 14
    8. x 2 + 3 x = 4 x squared , plus 3 x equals 4
    9. x 2 + 3 x = 2 x squared , plus 3 x equals 2
59. What is the discriminant of q x 2 + r x + s = 0 ? q , x squared , plus r x plus s equals 0 question mark
    1. qrs
    2. q 2 − 4 r s q squared , minus 4 r s
    3. r 2 − 4 q s r squared , minus 4 q s
    4. s 2 − 4 q r s squared , minus 4 q r

Short Response

60. What is a simpler form of x 2 ( 3 x 2 − 2 x ) − 3 x 4 ? x squared , open 3 , x squared , minus 2 x close minus 3 , x to the fourth , question mark  Classify the polynomial by degree and by number of terms.

Mixed Review

See Lesson 4-9.

Solve each system of equations.

61. { y = x 2 − 3 x − 7 y = − 2 x + 3 left brace . table with 2 rows and 1 column , row1 column 1 , y equals , x squared , minus 3 x minus 7 , row2 column 1 , y equals negative 2 x plus 3 , end table
62. { y = x 2 + x − 20 y = x 2 + 2 x left brace . table with 2 rows and 1 column , row1 column 1 , y equals , x squared , plus x minus 20 , row2 column 1 , y equals , x squared , plus 2 x , end table
63. { y = 3 x 2 + 8 x − 3 y = x 2 − 9 left brace . table with 2 rows and 1 column , row1 column 1 , y equals 3 , x squared , plus 8 x minus 3 , row2 column 1 , y equals , x squared , minus 9 , end table

See Lesson 2-4.

Write an equation of each line in standard form with integer coefficients.

64. y = 7 x + 0 . 4 y equals 7 x plus 0 . 4
65. y = − 3 x − 2 . 5 y equals negative 3 x minus 2 . 5
66. y = − 2 7 x + 4 y equals negative , 2 sevenths , x plus 4
67. y = 1 . 2 x − 0 . 5 y equals 1 . 2 x minus 0 . 5

Get Ready! To prepare for Lesson 5-2, do Exercises 68–70.

See Lesson 4-4.

Factor each quadratic expression.

68. x 2 + 7 x + 12 x squared , plus 7 x plus 12
69. x 2 + 8 x − 20 x squared , plus 8 x minus 20
70. x 2 − 14 x + 24 x squared , minus 14 x plus 24

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