word problem

Question

1. What are the zeros of a graph and how do you find them by graphing? Provide complete details and answer in a complete sentence.

2. Two physics students built a model rocket for a class project. Once the rocket is launched, its height in feet, h(t), can be found using the height function

h(t) = -16t² + 96t where t represents time in seconds. Find the time when the rocket finally hits the ground. Explain how you solved this problem.

3. A model rocket is launched upward and it follows a parabolic shape until it finally falls to the ground. You are asked to find the maximum height of the rocket by graphing. You cannot just graph and "trace the curve" to find the answer. Explain why, specify which calculator function you would need to use, and how it is done.

Answer 1

1)

 

The zeros of a graph is the point on the x-axis.  It is also the x values that make the y value to be zero.

 

 

2)

 

Set   h(t)=0 and solve for t.

 

-16t² + 96t = 0

 

 

Choose the positive value of t.   If you have 2 positive values of t, then choose the larger t value.

 

 

3)

 

You cannot simply trace the curve because the graph may be very narrow.  It will take forever to find the maximum.  Also, the maximum you get may not be the actual maximum.  Rather an estimate.  To find the exact value of the maximum, perform the following.

 

a) Press Y=

b) Enter the function described

c) Press GRAPH

d) Press 2ND and CALC

e) Scroll down maximum

f) Choose your left and right bounds near the peak.

e) Press ENTER.  The calculator will give you the x and y coordinate at the bottom of the screen.  That coordinate is your maximum.