Question

Algebra 2 help fan and medal help me plzzz

Answer 1

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

Answer 2

My equation x^3+3x^2-26x-84

Answer 3

@perl @Samus_Aran

Answer 4

i would need to see the entire question

Answer 5

ok

Answer 6

The rollercoaster will run from right to left, so work in that order when selecting points.
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 pasth 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 function 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 7

i already did 1 and 3 i just need help with two

and the ? are just there they just appeared when i copied and pasted them

Answer 8

hmm

Answer 9

can you upload the original document or worksheet

Answer 10

ummm yeah

Answer 11

thats it with what my answers are so far

Answer 12

ok one sec

Answer 13

here is an older response
http://openstudy.com/study#/updates/532476f8e4b087b3d40f8a72

Answer 14

Here is one I found
https://answers.yahoo.com/question/index?qid=20140620131439AAZMNJQ

Answer 15

i looked at those and they didnt apply to my equatiuon so i was confused

Answer 16

given the zeros, you can give the general form of polynomial
f(x)=a(x+7)(x+2)(x-6)

Answer 17

ok lol idk what the 2 rules are so could you explain the question to me plz

Answer 18

ok

Answer 19

we want to prove that your function matches the graph of the rollercoaster

Answer 20

yeah

Answer 21

you have a problem with your function.
I got
y=(x+7)(x+2)(x-6) = x^3+3 x^2-40 x-84

Answer 22

(x+7)(x+2)(x-6) =
=(x^2 + 7x + 2x + 14) ( x - 6)
=( x^2 + 9x + 14) ( x - 6)
= x^3 + 9x^2 + 14x - 6x^2 -54x - 84
= x^3 + 3x^2 - 40x - 84

Answer 23

hmmm

Answer 24

you made a mistake somewhere

Answer 25

i guess lol

Answer 26

so what next

Answer 27

also I would multiply by a factor to vertically compress or shrink it

Answer 28

ok so wb for question 2

Answer 29

so what does wb stand for

Answer 30

what about

Answer 31

ok

Answer 32

so you want to multiply your function by 1/20

Answer 33

y = 1/20 ( x^3 + 3x^2 - 40x - 84)

Answer 34

for number 2??

Answer 35

still for number 1

Answer 36

im looking for a number that goes nicely into 84 and those numbers

Answer 37

i already did number one lol can you help me with number 2 plzzzz

Answer 38

@shereenkhan

Answer 39

your graph is a bit extreme

Answer 40

ik i changed it

Answer 41

ok

Answer 42

i mean, it would be too steep

Answer 43

yeah lol i fixed it

Answer 44

@gorv

Answer 45

First of all, the Fundamental Theorem of Algebra guarantees that f(x) has at least one real root (one real x intercept )

Answer 46

ok

Answer 47

we're not really going to use the FTA much here (fund. theorem of algebra), but you can mention that the FTA guarantees 3 complex roots (imaginary roots come in pairs, so you have to have one real root )

Answer 48

the descartes rule of signs , we look at f(x) and f(-x), and count the number of sign changes

Answer 49

f(x) = x^3 + 3x^2 - 40x - 84 , this has one sign change

Answer 50

f(x)= x^3+3x^2-26x-84
we check the sign change happen from left to right
here is only one sign change + to -

Answer 51

now for f(-x)=-x^3+3x^2+26x-84
here 2 sign change are there

Answer 52

ok idk what to write for the answer ecause im noy sure what its asking

Answer 53

can you give me an example of hat youd right plz???

Answer 54

it goes from + to - , just once. so the number of positive real zeros are 1 or less by a multiple of 2. but you cant subtrat 1 by a multiple of 2 , you will get -1 , -3 , -5 , etc

Answer 55

what lol im so confused

Answer 56

we are given point
6 , -7 and -2
f(x) = (x - 6)(x - (-2))(x - (-7))
= (x - 6)(x + 2)(x + 7)
= (x - 6)(x^2 + 9x + 14)
= x(x^2 + 9x + 14) - 6(x^2 + 9x + 14)
= x^3 + 3x^2 - 40x - 84.
so as it is of degree 3 so it will have 3 zeros
As for Descartes' Rule of signs:
Since f(x) has 1 sign change, f has exactly 1 positive zero.

Moreover, f(-x) = -x^3 + 3x^2 + 40x - 84 also has 2 sign changes.
So, f has either 2 or 0 negative zeros.

as f(-2) = 0 and f(-7) = 0, we see that f indeed has exactly 2 negative zeros.)

Answer 57

ok ty!! so wb fta

Answer 58

the fta just says there are possible at most 3 real zeroes ,

Answer 59

3 x intercepts

Answer 60

ok so how do i write that in an answer??

Answer 61

this is a good explanation of descartes rule of signs
http://mathworld.wolfram.com/DescartesSignRule.html

Answer 62

you can mention that since the polynomial has degree 3 (highest exponent is 3) we will have a maximum of 3 x intercepts (we can't have more than 3 x intercepts, but we could have less then 3 )

Answer 63

the FTA gives us some information about the graph, just by the degree . but to narrow it down further we use Descartes law of signs

Answer 64

so in other words, the foreman is skeptical that your polynomial function accurately graphs the rollercoaster. the foreman might wonder, what if your function has more than three x-intercepts , maybe it has 4 or 5. you tell him, thats not possible by the FTA

Answer 65

you dont really have to say much about the FTA, just one sentence.