So my teacher has asked us to create an equation for a "roller coaster" that has the following requirements:

Question

-Your coaster ride must have at least 3 relative maxima and/or minima -the ride length must be at least 4 minutes -the coaster ride starts at 250 feet The ride dives below the ground into a tunnel at least once

Answer 1

Since you have 3 local extremas, you will have a polynomial function of degree 4.  The domain of the function is [0, 4].
 
Use these initial conditions as your guidelines:
 
f(0) = 250
 
f(x) has at least one x-intercept (crosses the x-axis) and must be in the interval (0, 4].

 

f(x) decreases in any of the following intervals: (0, 1) or (2, 3)

 

 

Remember, you will have an arbitrary function that satisfies these conditions.