C Challenge

26. Reasoning Write a quadratic function y = a x 2 + b x + c y equals , eh x squared , plus b x plus c  whose graph passes through the points (0, 7), (2, 13), and (4, 35).

27. Reasoning The diagram below shows the differences for the cubic function f ( x ) = x 3 − 2 x + 5 f open x close equals . x cubed , minus 2 . x plus 5  for the x-values 0, 1, 2, 3, 4, and 5.

    
    Image Long Description

    1. Write the second and third differences in the appropriate locations in the diagram.
    2. What do you predict the third difference would be if f (6) were added to the diagram?
    3. Do you think that the third differences will be constant for other cubic functions? Explain why or why not.

Standardized Test Prep

SAT/ACT

28. The graph below shows the number y of visitors to a museum over x days. Which function models the number of visitors?

    

    1. y = − 100 x + 900 y equals negative 100 x plus 900
    2. y = 900 ( 0.875 ) x y equals 900 . open , 0.875 , close to the x
    3. y = − 100 x + 800 y equals negative 100 x plus 800
    4. y = − 50 x 2 − 400 x + 1300 y equals negative , 50 x squared , minus 400 x plus , 1300
29. Which expression is equivalent to ( 4 x 3 + 2 x 2 + 1 ) + ( 3 x 2 + 8 x + 2 ) ? open , 4 x cubed , plus , 2 x squared , plus 1 close plus open , 3 x squared , plus 8 x plus 2 close question mark
    6. 7 x 2 + 10 x + 3 7 x squared , plus 10 x plus 3
    7. 7 x 3 + 10 x 2 + 3 x 7 x cubed , plus , 10 x squared , plus 3 x
    8. 4 x 3 + 5 x 2 + 3 4 x cubed , plus , 5 x squared , plus 3
    9. 4 x 3 + 5 x 2 + 8 x + 3 4 x cubed , plus , 5 x squared , plus 8 x plus 3

30. Which line passes through the point (1, 3) and is parallel to the line graphed below?

    

    1. y = 2 x + 1 y equals 2 x plus 1
    2. y = 2 x + 3 y equals 2 x plus 3
    3. y = 2 x − 5 y equals 2 x minus 5
    4. y = − 5 x + 8 y equals negative 5 x plus 8

Short Response

31. What are the factors of 10 x 2 − x − 2 ? 10 x squared , minus x minus 2 question mark  Show your work.

Mixed Review

See Lesson 9-6.

Use the quadratic formula to solve each equation. If necessary, round to the nearest hundredth.

32. 4 x 2 + 4 x − 3 = 0 4 x squared , plus 4 x minus 3 equals 0
33. x 2 + 2 x − 7 = 0 x squared , plus 2 . x minus 7 equals 0
34. 3 x 2 − 8 x = − 1 3 x squared , minus 8 x equals negative 1

Get Ready! To prepare for Lesson 9-8, do Exercises 35–37.

See Lesson 6-3.

Solve by elimination.

35. x + y = 10 x − y = 2 table with 2 rows and 2 columns , row1 column 1 , x plus y , column 2 equals 10 , row2 column 1 , x minus y , column 2 equals 2 , end table
36. 5 x − 6 y = − 32 3 x + 6 y = 48 table with 2 rows and 2 columns , row1 column 1 , 5 x minus 6 y , column 2 equals negative 32 , row2 column 1 , 3 x plus 6 y , column 2 equals 48 , end table
37. − 2 x + 15 y = − 32 7 x − 5 y = 17 table with 2 rows and 1 column , row1 column 1 , negative 2 x plus 15 y equals negative 32 , row2 column 1 , 7 x minus 5 y equals 17 , end table

Table of Contents