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# 4.05

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## austin jimenez

on 26 March 2015

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#### Transcript of 4.05

4.05
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.
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
To find the polynomial function I use the zeros set to x and multiply them all together. using foil (x-6)(x+2)(x+7)
(x2-4x-12)(x+7)
x3+3x2-40x-84
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.
To solve for the y-intercept I just need to plug zero into the x's
(0)3+3(0)2-40(0)-84=-84
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___

Assignment 4.05

Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your function matches your graph. Use complete sentences.
according to the fundamental theorem since this functions leading degree is three zeros which matches the function and how the graph looks like it will be laid out
Using Descartes rule of signs I can prove that
there are the right amount of positive/negative zeros
-
x3+3x2-40x-84
there is one sign change so there is one positive root
- -
-x3+3x2+40x-84
there are two changes so there are 2 or zero negative roots
This agrees with the information already give to me about the zeros 1 positive and 2 negatives
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