Problem 2 An Apache trout, which can jump upwards of 2 feet out of the water, has just started a jump. The function

h=f(t)=−12(t−3)2+2

represents the height,
h
(in feet), of the trout above the water where
t
is the time in seconds since the fish began its jump.

Part a)

Graph this function in an appropriate window. (Make sure to include all important points, and label appropriately.)

Part b)

Based on your graph, how long is the fish out of water? How do you know?

Part c)

A hawk is hunting for the trout and starts to dive out of the sky at the same time the fish starts its jump to catch the fish midair. The hawk’s dive can be modeled by the function

d=f(t)=−1.5(t−4.5)+0.875

where
d
represents the height of the hawk in feet above the water. Add this function to your graph from Part a) and include the new graph here. (Make sure to include all important points, and label appropriately.)
Part d)

Based on your graph, when does the hawk catch the fish? How do you know?

Part e)
The equation that represents the hawk’s height as a function of time since the fish jumped is a linear function. What is the slope of the equation and what does it represent in context of the problem?