The height of a baseball, in feet, is modeled by a function, , given by the equation . The graph of the function is shown.

1. About when does the baseball reach its maximum height?
2. About how high is the maximum height of the baseball?
3. About when does the ball hit the ground?

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.

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Technology required. Two rocks are launched straight up into the air. The height of Rock A is given by function , where . The height of Rock B is given by function , where . In both functions, is time measured in seconds and height is measured in feet.

Use graphing technology to graph both equations. Determine which rock hits the ground first and explain how you know.

Each expression represents an object’s distance from the ground, in meters, as a function of time, , in seconds.

Object A:

Object B:

1. Which object was launched with the greatest vertical speed?
2. Which object was launched from the greatest height?

Here is a pattern of dots.

1. Complete the table.
2. How many dots will there be in Step 10?
3. How many dots will there be in Step ?

step	total number of dots
0
1
2
3

A function, , is defined by , and a function, , is defined by .

1. Find the values of and when is 4, 5, and 6.
2. Are the values of always greater than the values of , for all ? Explain how you know.

Han accidentally drops his water bottle from the balcony of his apartment building. The equation gives the distance from the ground, , in meters, that his water bottle is after seconds.

1. Complete the table, and then plot the data on the coordinate plane.

   (seconds)	(meters)
   0
   0.5
   1
   1.5
   2

   

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2. Is the water bottle falling at a constant speed? Explain how you know.