Question

As one of the new rollercoaster engineers, you have been tasked with developing a rollercoaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the rollercoaster 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 rollercoaster crosses the x–axis. Precise measurements and attention to detail are very important.

Answer 1

First, here is the existing map of current structures. It is important that the rollercoaster does not go through the foundation of any of these structures.

1st point: ___6___
2nd point:___-2___
3rd point: ___-7___

1.Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your rollercoaster. Show all of your work.


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


3.Solve for the y–intercept for your function, f(x), and then construct a rough graph of your rollercoaster. If your y–intercept is off the graph, give the coordinates of the y–intercept.

Answer 2

given the zeros, you can give the general form of polynomial
\[f(x) = a(x+7)(x+2)(x-6)\]
From the description, the end behavior is decreasing, so you can assume that a < 0
Now you need an "a" that will make the graph not hit the buildings in any way

To do that lets look at middle building, the graph should be higher than point (-1,3) to clear and higher than (4,3) to clear other side

plug in x=-1, set equal to 3, solve for a
\[a = -\frac{3}{42} = -\frac{1}{14}\]
plug in x=4, set equal to 3, solve for a
\[a = -\frac{3}{132} = -\frac{1}{44}\]

So "a" needs to be less than -1/14 to clear the buildings. Lets make it -1/10 to be safe
final equation
\[f(x) = -\frac{1}{10}(x+7)(x+2)(x-6)\]
to find y-intercept, plug in x=0
--> (0, 8.4)

Answer 3

http://www.wolframalpha.com/input/?i=plot+-.1%28x%2B7%29%28x%2B2%29%28x-6%29+from+x+%3D+-12+to+12+from+y%3D-10+to+15

Answer 4

The information included in this question is the intellectual property of Florida Virtual School. Posting questions from any FLVS course and receiving answers is considered cheating.

Answer 5

hhaahahaha your funny @dashreeve