Math 3 – Module 3 Polynomial Roller Coaster Problem #6 Name: Period: Date: _______________________________________________________________________________________________ Paola, Lucia, Francisco, and Sergio decide to visit an amusement park because they like to ride roller coasters. While waiting in line Lucia notices that part of this roller coaster resembles the graph of a polynomial they recently studied in their Math 3 class. The brochure for the roller coaster says that, for the first 10 seconds of the ride, the height of the coaster can be determined by ℎ 𝑡 = −0.39𝑡 ! + 6𝑡 ! − 27𝑡 ! + 39𝑡, where t is the time in seconds and h is the height in feet. 1. a What is the degree of the polynomial? 2. b. Where does the roller coaster start from? 2. Use the graphing calculator to approximate the roots, relative maxima and minima of this function to sketch the graph of the function over the first 10 seconds. Round your answers to three decimal places. 3. Use the points you found in question 2 as well as the y-­‐intercept to sketch the graph of the function over the first 10 seconds. 4. a. Use interval notation to describe the intervals over which the function is increasing and decreasing. 4. b. State the domain and range in the context of the problem. 5. Clearly describe the end behavior of this function (without context) and the reason for this behavior. 6. Suppose that this coaster is a 2 minute ride, do you believe that ℎ 𝑡 = −0.39𝑡 ! + 6𝑡 ! − 27𝑡 ! + 39𝑡 is a good model for the height of the roller coaster throughout the ride? Clearly explain and justify your response.