Introduction: As aspiring structural engineers specializing in roller coaster design, you are about to embark on an exhilarating journey to create your very own roller coaster ride. To complete this task successfully, you'll need to follow a structured set of steps provided by the amusement park. Your mission is to craft an exceptional roller coaster that fulfills the following requirements: 5. Verification (10 pts) 1. Your coaster must feature at least 3 relative maxima and/or minima. Use long division and/or synthetic division to verify the correctness of your 2. The ride must have a minimum duration of 4 minutes. equation, focusing on one of your roots. 3. The roller coaster should commence at a height of 250 feet. 6. End Behavior (15 pts) 4. The ride must include a segment where it descends below the ground into a tunnel. Describe the end behavior of your function. Provide a reasoned explanation for this behavior based on the roller coaster's design and physics. Project Tasks: 7. Graphical Representation (15 pts) 1. Design Your Roller Coaster (15 pts) Create an accurate graph of your polynomial function. Create a rough sketch of your roller coaster ride on a coordinate plane. 8. Conclusion (10 pts) Ensure your design clearly features the x-axis and y-axis, providing accurate scales What did you learn by completing this project that you might use in solving other for ride length and height. problems in the future? Verify that your design adheres to the specified criteria, 2. Identify and Define Zeros (15 pts) List all the zeros or roots of your roller coaster polynomial. Include at least one double root (multiplicity of two), a minimum of 2 real roots, and imaginary roots. Modify your original design as necessary to meet these root requirements. 3. Write Factored Form (10 pts) Express your roller coaster polynomial in its complete factored form. Feel free to invent an imaginary root (e.g., 2i), but remember that imaginary roots come in conjugate pairs. 4. Standard Form Equation (10 pts) Determine the equation in standard form that represents your roller coaster ride