You have decided to become a structural engineer who specializes in roller coaster design.

Your job is to design your own roller coaster ride. To complete this task, please follow these steps:

The amusement park you are designing for gave you the following coaster requirements:

- your roller 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 750 meters

- the ride dives below the ground into a tunnel at least once

1. Draw a rough sketch of your "roller coaster" ride on a coordinate plane.

Note: Be sure to illustrate your x-axis and y-axis scale to identify the length of the ride and the height of the ride you are designing. Make sure your design meets all the criteria listed above.

2. List all zeros or roots of your polynomial; be sure to include at least one of each of the following on your design: one double root (multiplicity of two), at least 2 real root, and imaginary roots.

It might be necessary to go back to your design and modify it according to these root requirements.

3. Write the complete factored form of your roller coaster polynomial.

4. Find the equation in standard form that represents your roller coaster ride.

5. Perform long division and/or synthetic division to verify the correctness of your equation.

6. If this roller-coaster was continuous, describe the end behavior of your function and give a reason for this behavior.

7. Draw an accurate graph of your polynomial.

8. Color the graph blue where the polynomial is increasing and red where the polynomial is decreasing and identify increasing, decreasing, and constant intervals.

9. Calculate the time it will take your rollercoaster to finish if the average speed of your rollercoaster is 180 m/s.

10. Does your rollercoaster design meet all the requirements of the amusement park? Provide a reason for your answer.