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 (x-axis) and the height of the ride (y-axis) you are designing. Make sure your design meets all the criteria listed above.
2. Calculate the distance of the roller coaster if the average speed of your rollercoaster is 40m/s.
3. 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) and 3 real roots.
It might be necessary to go back to your design and modify it according to these root requirements.
4. Write the complete factored form of your roller coaster polynomial.
5. Find the equation in standard form that represents your roller coaster ride.
6. Perform synthetic division to verify the correctness of your equation.
7. Draw an accurate graph of your polynomial.
8. Describe the end behavior of your function and give a reason for this behavior.
9. Color the graph blue where the polynomial is increasing and red where the polynomial is decreasing and identify increasing, decreasing, and constant intervals.
10. Does your rollercoaster design meet all the requirements of the amusement park? Provide a reason for your answer.
