C Challenge

28. Reasoning What is the minimum number of data points you need to find a single quadratic model for a data set? Explain.
29. A parabola contains the points ( 0 , − 4 ) , open 0 comma negative 4 close comma  (2, 4), and (4, 4). Find the vertex.
30. A model for the height of an arrow shot into the air is h ( t ) = − 16 t 2 + 72 t + 5 , h open t close equals negative 16 , t squared , plus 72 t plus 5 comma  where t is time and h is height. Without graphing, answer the following questions.
    1. What can you learn by finding the graph's intercept with the h-axis?
    2. What can you learn by finding the graph's intercept(s) with the t-axis?

Standardized Test Prep

SAT/ACT

31. The graph of a quadratic function has vertex ( − 3 , − 2 ) . open negative 3 comma negative 2 close .  What is the axis of symmetry?
    1. x = − 3 x equals negative 3
    2. x = 3 x equals 3
    3. y = − 2 y equals negative 2
    4. y = 2 y equals 2
32. Which function is NOT a quadratic function?
    6. y = ( x − 1 ) ( x − 2 ) y equals open x minus 1 close open x minus 2 close
    7. y = x 2 + 2 x − 3 y equals , x squared , plus 2 x minus 3
    8. y = 3 x − x 2 y equals 3 x minus , x squared
    9. y = − x 2 + x ( x − 3 ) y equals negative , x squared , plus x open x minus 3 close
33. Which is the composition f (g(x)), if f ( x ) = − x − 3 f open x close equals negative x minus 3  and g(x) = 7 + 5x?
    1. f(g(x)) = 4x + 4
    2. f ( g ( x ) ) = 4 x − 10 f open g open x close close equals 4 x minus 10
    3. f ( g ( x ) ) = − 5 x − 8 f open g open x close close equals negative 5 x minus 8
    4. f ( g ( x ) ) = − 5 x − 10 f open g open x close close equals negative 5 x minus 10

    Extended Response

34. Mark has 42 coins consisting of dimes and quarters. The total value of his coins is $6. How many of each type of coin does he have? Show all your work and explain what method you used to solve the problem.

Mixed Review

See Lesson 4-2.

Graph each function.

35. y = x 2 − 6 x − 3 y equals , x squared , minus 6 x minus 3
36. y = 2 x 2 + 9 x − 4 y equals , 2 x squared , plus 9 x minus 4
37. y = 3 x 2 − 4 x + 1 y equals , 3 x squared , minus 4 x plus 1

See Lesson 3-2.

Solve each system by elimination.

38. { x + y = 7 5 x − y = 5 left brace . table with 2 rows and 2 columns , row1 column 1 , x plus y , column 2 equals 7 , row2 column 1 , 5 x minus y , column 2 equals 5 , end table
39. { 2 x − 3 y = − 14 3 x − y = 7 left brace . table with 2 rows and 3 columns , row1 column 1 , 2 x minus , column 2 3 y , column 3 equals negative 14 , row2 column 1 , 3 x minus , column 2 y , column 3 equals 7 , end table
40. { x − 3 y = 2 x − 2 y = 1 left brace . table with 2 rows and 1 column , row1 column 1 , x minus 3 y equals 2 , row2 column 1 , x minus 2 y equals 1 , end table

See Lesson 2-2.

For Exercises 41–42 y varies directly with x.

41. If y = 2 when x = 5, find y when x = 2.
42. If y = − 2 y equals negative 2  when x = 4, find y when x = 7.

Get Ready! To prepare for Lesson 4-4, do Exercises 43–45.

See Lesson 1-3.

Simplify by combining like terms.

43. x 2 + x + 4 x − 1 x squared , plus x plus 4 x minus 1
44. 6 x 2 − 4 ( 3 ) x + 2 x − 3 6 x squared , minus 4 open 3 close x plus 2 x minus 3
45. 4 x 2 − 2 ( 5 − x ) − 3 x 4 x squared , minus 2 open 5 minus x close minus 3 x

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