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Practice

7.14.6 Practice

7.14.6 • Practice

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

  1. Here are graphs of functions f and g .

    Each represents the height of an object being launched into the air as a function of time.

Graphs of functions f and g. Vertical axis, height. Horizontal axis, time. Function f begins low on the y axis, increases in height quickly, then ends at about halfway down the x axis. Function g begins high on the y axis, moves gradually downward, and ends toward the end of the x axis.

    1. Which object was launched from a higher point?
  1. The object represented by function g
  2. The object represented by function f
    1. Which object reached a higher point?
  1. The object represented by function g
  2. The object represented by function f
    1. Which object was launched with the greater upward velocity?
  1. The object represented by function g
  2. The object represented by function f
    1. Which object landed last?
  1. The object represented by function g
  2. The object represented by function f
  1. The function h given by h ( t ) = ( 1 − t ) ( 8 + 16 t ) models the height of a ball in feet, t seconds after it was thrown.
    1. Find one of the zeros of the functions using ( 8 + 16 t ) .
    1. Find one of the zeros of the functions using ( 1 − t ) .
    1. What do the zeros tell us in this situation?
  1. The negative zero represents the time, in seconds, when the basketball is on the ground or hits the ground.
  2. The positive zero represents the time, in seconds, when the basketball reaches the maximum height.
  3. The negative zero represents the height, in feet, when the time is zero.
  4. The positive zero means the time, in seconds, when the basketball is on the ground or hits the ground.
    1. Are both zeros meaningful?
  1. Yes
  2. No
    1. From what height, in feet, is the ball thrown?
    1. When, in seconds, does the ball reach its highest point?
    1. How high, in feet, does the ball go?
  1. The height in feet of a thrown football is modeled by the equation f ( t ) = 6 + 30 t − 16 t 2 , where time t is measured in seconds.
    1. Which term in the equation describes how many feet above the ground the football was thrown?
  1. The squared term 16 t 2
  2. The squared term − 16 t 2
  3. The linear term 30 t
  4. The constant term 6
    1. Which term in the equation describes the initial upward velocity of the football in feet per second?
  1. The squared term 16 t 2
  2. The squared term − 16 t 2
  3. The linear term 30 t
  4. The constant term 6
    1. How does the squared term − 16 t 2 affect the value of the function f ?
  1. The value of the function is zero when − 16 t 2 is zero.
  2. The squared term has no effect on the value of the function.
  3. The squared term increases the value of the function.
  4. The squared term decreases the value of the function.
    1. What does this term − 16 t 2 reveal about the situation?
  1. How long the ball is in the air before it hits the ground.
  2. How far the football was thrown above the ground.
  3. The initial upward velocity of the football.
  4. The influence of gravity pulling the ball down to the ground.
  1. The height in feet of an arrow is modeled by the equation h ( t ) = ( 1 + 2 t ) ( 18 − 8 t ) , where t is seconds after the arrow is shot.
    1. At what time, in seconds, does the arrow hit the ground?
    1. At what height, in feet, is the arrow shot?
  1. Two objects are launched into the air.

  • The height, in feet, of Object A is given by the equation f ( t ) = 4 + 32 t − 16 t 2 .

  • The height, in feet, of Object B is given by the equation g ( t ) = 2.5 + 40 t − 16 2 .

  • In both functions, t is seconds after launch.

    1. Which object was launched from a greater height?
  1. Object A
  2. Object B
    1. Which object was launched with a greater upward velocity?
  1. Object A
  2. Object B