1. Every year Newton High School a water balloon competition during half time of the
football game. Each person gets a chance to launch water balloons at a target. Here is
the data of one of the fallowing participants.
Time (in Seconds) after the balloon launched
0
2
3
4
5
6
7
8
9
Height in feet off the ground
0
9
16
21
25
24
19
15
0
a. Use your calculator to find the equation that best fits the data.
b. Give the theoretical domain and range of the data.
c. Give the practical domain and range of the data.
d. Using your model how high is the balloon at 5.5 seconds after it is launched.
e. Using you model, estimate the time(s) when the balloon is at least 22 feet of the ground.
f. What is the average rate of change from x = 4 seconds to x = 7 seconds?
g. Using the intercepts and anther point find the equation by hand.
2. The height of a gymnast’s bounce above a trampoline is given by the table.
Time into bounce(in Seconds)
0
0.1
0.6
1.1
1.3
1.5
Height above trampoline (feet)
0
.8
6.3
7.8
1.2
0
a. Use your calculator to find the equation that best fits the data.
b. Give the theoretical domain and range of the data.
c. Give the practical domain and range of the data.
d. Using your model how high is the balloon at 0.8 seconds after it is launched.
e. Using you model, estimate the time(s) when the balloon is at least 0.5 feet of the ground.
f. What is the average rate of change from x = 0.1 seconds to x =1.3 seconds?
g. Using the intercepts and anther point find the equation by hand.
3. Through the 2007–2008 season, Mark Price had the best ever lifetime free-throw
percentage in the National Basketball Association at 0.904. The path of the basketball
can be modeled by the equation ℎ(𝑑) = −16𝑑 2 + 22𝑡 + 6.2, where d is the horizontal
distance in feet and h(d) is the height of the ball in feet.
a. What is the meaning of each coefficient in the equation?
b. Find the zero(s)? What does that value(s) represent?
4. When a punkin’ chunker launches a pumpkin, the goal is long distance, not height.
Suppose the relationship between horizontal distance d (in feet) and time t (in seconds) is
given by the function rule d = 70t, when the height is given by ℎ = 20 + 50𝑡 − 16𝑡 2 .
a. How long will the pumpkin be in the air?
b. How far will the pumpkin travel from the chunker by the time it hits the ground?
c. When will the pumpkin reach its maximum height, and what will that height be?
d. How far from the chunker will the pumpkin be (horizontally) when it reaches its maximum
height?
The opening of the cannon pictured at the left is 16 feet above the ground. The daredevil,
who is shot out of the cannon, reaches a maximum height of 55 feet after about 1.56 seconds
and hits a net that is 9.5 feet off the ground after 3.25 seconds. Use this information to
answer the following questions.
a. Write a rule that relates the daredevil’s height above the ground h at a time t seconds after
the cannon is fired.
b. At what upward velocity is the daredevil shot from the cannon?
c. If, for some unfortunate reason, the net slipped to the ground at the firing of the cannon,
when would the daredevil hit the ground?