Question

Welcome to Oakville Lake Amusement Park!
As one of the new roller coaster engineers, you have been tasked with developing a roller coaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the roller coaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground. There must be three distinct points where the roller coaster crosses the x–axis. Precise measurements and attention to detail are very important.


First, here is the existing map of current str

Answer 1

First, here is the existing map of current structures. It is important that the roller coaster does not go through the foundation of any of these structures.
1st point: ___6___2nd point:___-2___3rd point: ___-7___
Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your roller coaster. Show all of your work.

(x-6)(x+2)(x+7
(x-6)(x^2+9x+14)
x(x^2+9x+14)-6(x^2+x+14)
f(x)=x^3+3x^2-40x-84


Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your function matches your graph. Use complete sentences.

So for the Fundamental Theorem of Algebra it is used to find the number of the complex zeros to the function There is a total of 2 complex 0s. And for Descartes rule of signs it says since f(x)will have 1 sign change, f would have 1 positive zero. So for f(-x)= -x^3+3x^2+40x-84 it would have 2 sign changes as stated by the Descartes rule. Then f has either 2 or 0 negative zeros.




Solve for the y–intercept for your function, f(x), and then construct a rough graph of your roller coaster. If your y–intercept is off the graph, give the coordinates of the y–intercept.
For this we can set it to x=0. After this the y interceptis f(0)=-84

Answer 2

So i just need to make a graph how do i do that about this