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. (Hint: Are there only x-axis intercepts? How many times can a function cross the y-axis?) 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+2)(x-1)(x-2) g(x)=(x+3)(x+2)(x-3) g(x)=(x+2)(x-2)(x-3) g(x)=(x+5)(x+2)(x-5) g(x)=(x+7)(x+1)(x-1) Create a graph, either by hand or using the using software of your choice, of the polynomial function you selected from Question 2. Copy and paste your graph below: Part B The second part of the new coaster is a parabola Ray needs help creating the second part of the coaster. Create a unique parabola in the patternf(x)=(x-a)(x-b). Describe the direction of the parabola and determine the y-intercept and zeros. Create a unique parabola in the pattern f(x)=(x-a)(x-b). Pick integers other than one or zero for a and b. Describe the direction of the parabola. (Hint: How can you tell if a parabola will open upwards or downwards) Determine the y-intercept. (Hint: Using your equation, set the x’s equal to zero and solve for y) Determine the zeros. (Hint: Using your equation, set y = zero, factor, and solve for x. Create a graph, either by hand or using the using software of your choice, of the parabola you created from Question 4. Copy and paste your graph below: Part C 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. (Note: Once you combine your sections, it should look like a roller coaster) Part D 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