Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track. Part A The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer. (THIS ANSWER IS IN MY VIDEO) - PLEASE TYPE ANSWERS HERE. 2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros. g(x)=x-x - 4x + 4 (FACTOR THIS - HINT: FACTOR BY GROUPING) after you factor, set each factor = 0 and solve these are your zero's. to get the y intercept- set all x's = 0 and solve - that is your y-intercept Watch my video for end behavior - the leading coefficient of this polynomial is x^3 (POSITIVE (no negative) and ODD (exponent is 3 which is odd- WHAT IS POSITIVE ODD END BEHAVIOR? 3. Create a graph of the polynomial function you selected from Question 2 INSERT YOUR TRINOMIAL GRAPH HERE. GO TO DESMOS.COM AND PUT IN THE ABOVE POLYNOMIAL---COPY IT AND PASTE IT HERE. VIDEO ON HOW TO DO THIS IS ABOVE. Part B The second part of the new coaster is a parabola. 4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros. 5. The safety inspector notes that you also need to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of your parabola, and show your work. 6. Create a graph of the polynomial function you created in Question 4. INSERT YOUR GRAPH OF THE PARABOLA HERE! Part C 7. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view. COMBINE BOTH GRAPHS HERE! Do not do this part Part D 8. Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.