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Algebra 1

7.6.5 Practice

Algebra 17.6.5 Practice
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Complete the following questions to practice the skills you have learned in this lesson.

  1. The height of a diver above the water is given by h ( t ) = − 5 t 2 + 10 t + 3 , where t is time measured in seconds and h ( t ) is measured in meters. Select two statements that are true about the situation.
  1. The diver begins 5 meters above the water.
  2. The diver begins 3 meters above the water.
  3. The function has 1 zero that makes sense in this situation.
  4. The function has 2 zeros that make sense in this situation.
  5. The graph that represents h starts at the origin and curves upward.
  6. The diver begins at the same height as the water level.
  1. The height of a baseball, in feet, is modeled by the function h given by the equation h ( t ) = 3 + 60 t − 16 t 2 . The graph of the function is shown.

A curve on a graph, origin O, with grid. Horizontal axis, time, seconds, scale 0 to 8, by 1’s. Vertical axis, height, feet, scale 0 to 200, by 20’s. A curve passes through the points 0 comma 3, 2 comma 59, and 3 comma 36.

    1. About when does the baseball reach its maximum height? Round to the nearest second.
    1. About how high is the maximum height of the baseball? Round to the nearest ten.
    1. When does the baseball hit the ground? Round to the nearest second.
  1. Two rocks are launched straight up in the air. The height of Rock A is given by the function f , where f ( t ) = 4 + 30 t − 16 t 2 . The height of Rock B is given by g , where g ( t ) = 5 + 20 t − 16 t 2 . In both functions, t is time measured in seconds and height is measured in feet.

The following is a graph of the functions. Use the graph to answer the questions a – c.

    1. Which graph is the height of Rock A, f ( t ) = 4 + 30 t − 16 t 2 ?
  1. Green Graph
  2. Red Graph
    1. Which graph is the height of Rock B, g ( t ) = 5 + 20 t − 16 t 2 ?
  1. Green Graph
  2. Red Graph
    1. Determine which rock hits the ground first.
  1. Rock B
  2. Rock A
  1. Each expression represents an object’s distance from the ground, in meters, as a function of time, t , in seconds.

Object A: − 5 t 2 + 25 t + 50

Object B: − 5 t 2 + 50 t + 25

  1. Which object was launched with the greater vertical speed?
  1. Object B
  2. Object A
  1. Which object was launched from the greater height?
  1. Object B
  2. Object A
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