C Challenge

41. Sports Suppose a tennis player hits a ball over the net. The ball leaves the racket 0.5 m above the ground. The equation h = − 4 . 9 t 2 + 3.8 t + 0.5 h equals negative 4 . , 9 t squared , plus 3.8 t plus 0.5  gives the ball's height h in meters after t seconds.
    1. When will the ball be at the highest point in its path? Round to the nearest tenth of a second.
    2. Reasoning If you double your answer from part (a), will you find the amount of time the ball is in the air before it hits the court? Explain.
42. The parabola below is of the form y = x 2 + b x + c . y equals , x squared , plus b x plus c .

    

    1. Use the graph to find the y-intercept.
    2. Use the graph to find the equation of the axis of symmetry.
    3. Use the formula x = − b 2 a x equals . fraction negative b , over 2 eh end fraction  to find b.
    4. Write the equation of the parabola.
    5. Test one point using your equation from part (d).

    6. Reasoning Would this method work if the value of a were not known? Explain.

Standardized Test Prep

SAT/ACT

43. A half-pipe ramp at a skate park is approximately parabolic in shape. It can be modeled by the quadratic function y = x 2 − 6 x + 9 . y equals , x squared , minus 6 x plus 9 .  At what point would a skater be at the lowest part of the ramp?
    1. ( − 3 , 36 ) open negative 3 comma 36 close
    2. ( 36 , − 3 ) open 36 comma negative 3 close
    3. (3, 0)
    4. (0, 3)
44. What is the simplified form of the product 4 ( − 8 ) ( 5 ) ( − 1 ) ? 4 open negative 8 close open 5 close open negative 1 close question mark
    6. − 160 negative 160
    7. − 80 negative 80
    8. 80
    9. 160
45. Which of the following is equivalent to ( − 4 ) 3 ? open negative 4 close cubed . question mark
    1. − 64 negative 64
    2. − 12 negative 12
    3. 12
    4. 64
46. Toby needs to write an example of the Commutative Property of Multiplication for his homework. Which of the following expressions could he use?
    6. a b = b a eh b equals b eh
    7. a = a eh equals eh
    8. a b = a b eh b equals eh b
    9. a ( b c ) = ( a b ) c eh open b c close equals open eh b close c

Short Response

47. Simplify the product ( 3 r − 1 ) ( 4 r 2 + r + 2 ) . open 3 r minus 1 close open , 4 r squared , plus r plus 2 close .  Justify each step.

Mixed Review

See Lesson 9-1.

Graph each function.

48. y = − x 2 − 2 y equals negative , x squared , minus 2
49. y = − 1 2 x 2 + 1 y equals negative , 1 half , x squared , plus 1
50. y = 2 x 2 + 7 y equals , 2 x squared , plus 7

Get Ready! To prepare for Lesson 9-3, do Exercises 51–54.

See Lessons 1-3 and 1-6.

Simplify each expression.

51. 25 square root of 25
52. − 64 negative square root of 64
53. ± 144 plus minus , square root of 144
54. 1.21 square root of 1.21

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