Question

HAVE to get this right or I'll fail? Algebra 1? I have the first part done, i just need the second part.

Answer 1

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.
1. Both Ray and Kelsay are correct because a third degree polynomial can have at most three x intercepts and always has  one y intercept. So it can have 4 intercepts and 3 zeroes. It cross the x three time and the y once or depending where the exponents are either on x or y it can cross the y three times and the x once.

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) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14
2. g(x) = x3 − x2 − 4x + 4
g(x) is large and positive when x is large and positive;
g(x) is large and negative when x is large and negative.
The y-intercepts are  4,  The zeroes are -2, 2, 1

Create a graph of the polynomial function you selected from Question 2.
I created graph, but I don't think I need to post it.

Answer 2

Those are my answers for the first part...those are needed to answer the second part, now I have a second part I need help on.

Answer 3

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 pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.

The safety inspector notes that Ray also needs 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 the parabola, showing your work, so Ray can include it in his coaster plan.

Create a graph of the polynomial function you created in Question 4.

Answer 4

Also... after x on everything, the next number is squared or to the power of that number. I forgot the ^ on them.

Answer 5

@Maddy1251 can you help?? This is important :(

Answer 6

@fabgirl1994 Still here!?