100 POINTS I anwered A and B i just need help with C Part A (ANSWERED)
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. 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 four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.

A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.

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.
o g(x) = (x + 2)(x − 1)(x − 2)
o g(x) = (x + 3)(x + 2)(x − 3)
o g(x) = (x + 2)(x − 2)(x − 3)
o g(x) = (x + 5)(x + 2)(x − 5)
o g(x) = (x + 7)(x + 1)(x − 1)

g(x) = x3 − x2 − 4x + 4

3. Create a graph of the polynomial function you selected from Question 2.

it has points at (-2, 0), (1, 0) and (2, 0). And the y-intercept is (0, 4).

Part B (ANSWERED)
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) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.

A unique parabola in the form f(x) = ax2 - bx + c could be… f(x) = 3x2 - 2x - 4. When you graph this equation, the direction of the parabola is first sloping down then curving at the bottom to start going back upwards. The y-intercept is -4.

1. Create a graph of the polynomial function you created in Question 4. the direction of the parabola is first sloping down, then curving at the bottom to start going back upwards. The y-intercept is -4.

Part C (HELP)

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.