Representing Quantities in a Situation

4.9.4 Representing Quantities in a Situation

4.9.4 • Representing Quantities in a Situation

Activity

Watch the video of the tennis ball being dropped.

The height of the ball is a function of time. Suppose the height is $h$ feet, $t$ seconds after the ball is dropped.

Create a table of values that displays the height of the tennis ball, in feet, at key moments during the video. To help you get started, use the still images to complete the table of values.

A person in a blue shirt and khaki pants stands sideways against a gray wall, holding a yellow tennis ball above their head with an outstretched arm at 0 seconds. At 0.28 seconds, the ball is approximately chest height of the man. At 0.54 seconds, the ball is on the ground. At 0.74 seconds, the ball is approximately knee height of the man. At 1.03 seconds, the ball is approximately waist height of the man. At 1.48 seconds, the ball is on the ground. At 1.88 seconds, the ball is approximately knee height of the man. At 2.25 seconds, the ball is on the ground.

Time (seconds)	Height (feet)
0	A. ______
0.28	B. ______
0.54	C. ______
0.74	D. ______
1.03	E. ______
1.48	F. ______
1.88	G. ______
2.25	H. ______

Compare your answer:

Time (seconds)	Height (feet)
0	A. 6
0.28	B. 4.3
0.54	C. 0
0.74	D. 2.2
1.03	E. 3.5
1.48	F. 0
1.88	G. 2
2.25	H. 0

2. Use a blank coordinate plane to sketch a graph of the height of the tennis ball as a function of time. Use the table of values you created to help guide your graph.

Hint: Suggestion for how to set up graph here.

Compare your answer:

Graph that shows height in feet as a function of time in seconds the height of the ball as a function of time is modeled by upside down parabolas the maximum heights of the parabolas decrease from left to right the first parabola has a maximum height at the point (0, 6).

3. Identify the horizontal intercepts ( $x$ -intercepts) of the graph. Explain what the coordinates tell us about the tennis ball.

Compare your answer:

$(0.54, 0)$ , $(1.48, 0)$ , and $(2.25, 0)$ are three of the horizontal intercepts. They represent the times at which the ball hits the ground.

4. Identify the vertical intercept ( $y$ -intercept) of the graph. Explain what the coordinates tell us about the tennis ball.

Compare your answer:

$(0, 6)$ is the $y$ -intercept. It is the height from which the tennis ball is dropped.

5. Find the maximum value of the function. Explain what it tells us about the tennis ball.

Compare your answer:

The maximum value of the function is 6, at $t = 0$ . The height from which the ball is dropped, 6 feet, is its greatest height.

6. Find the minimum value of the function. Explain what it tells us about the tennis ball.

Compare your answer:

The minimum value is 0, at multiple points when the tennis ball hits the ground.

Are you ready for more?

Extending Your Thinking

If you only see the still images of the ball and not the video of the ball bouncing, can you accurately graph the height of the ball as a function of time? Explain your reasoning.

Compare your answer:

No, each still image gives the position of the ball at a different time, or one point on the graph that represents height as a function of time. But without the video, we would not know what is happening at the time the image is taken: Is the ball going up? Is it coming down? Is it at one of its peaks?