Question

Polynomial Function?

Answer 1

u wont to kno what it is

Answer 2

No I needed help with this equation. x^4+2x^3+6x^2-3x-7

Answer 3

Then I'm supposed to describe the graph, but I'm reall stuck on how to solve this.

Answer 4

ya im in geometry so im pass that already holup

Answer 5

@phi @!Star!

Answer 6

gotta get someone who will be able to help you

Answer 7

Alright thank you :)

Answer 8

Both of them are offline.

Answer 9

Okay. So, with any equation you can find the y intercept by plugging 0 in for x. Thats an easy thing to describe on the graph right off the back.

Answer 10

Okay, can you help me through it. Are you saying all the xs?

Answer 11

Well, if you're truly lost you can try that. Just plugging in some numbers for the xs will give you a general idea of what the graph looks like, but with this type of problem my teachers would normally expect me to give them the x/y intercepts.

Answer 12

If all they're looking for is a description of the graph is, you can reason through it logically.

Answer 13

Okay hang on while I do the work.

Answer 14

The x^4 is the largest part of the polynomial, so it is going to be the dominant part of the graph.

Answer 15

And if you know that the equation ax^2 +bx +c looks like a parabola, then you can assume that the x^4 +.... will look similar.

Answer 16

So it'll probably look something like a parabola, with a minimum and two lines going upwards.

Answer 17

I'm sorry can you just do this step by step with the problem. I understand the graphing part but I do not get how to solve the polynomial function itsle.f

Answer 18

How do you mean solve it? I thought you only needed to describe the graph?

Answer 19

I do. The question says you are having a meeting with the CEO of a soda company. You have interpreted the number of cans of soda produced versus profit as the function p(x)= x^4+2x^3+6x^3-3x-7.

Answer 20

Ah, so you're like, interpreting it?

Answer 21

Describe to the CEO what the graph looks like. Use complete sentences and focus on the end behvaiors of the graph and where the company will break even (where p(x)=0)

Answer 22

Okay so 0=x^4+2x^3+6x^2-3x+7

Answer 23

*-7

Answer 24

Oh yeah. My bad

Answer 25

Just one moment. Been a while since I've done this.

Answer 26

Its cool :)

Answer 27

http://www.purplemath.com/modules/solvpoly.htm

Does that process look familiar?

Answer 28

Oh! So I have to use synthetic division? And just graph after that?

Answer 29

I believe so.

Answer 30

I see okay hold on.

Answer 31

I've been working at it, and there doesn't seem to be any reasonably easy to guess roots.

I'm guessing you aren't allowed to use your calculator?

Answer 32

They aren't asking me to divide. I was wrong that's not synthetic division.

Answer 33

So are you allowed to use calculators?

Answer 34

Cause if you use a computer/ calculator to graph it there are only 2 0s, neither of which are easy to factor out. There's some really long complicated equations for solving, but I doubt that your teacher/ professor would expect you to do them.

Answer 35

Alright I called my teacher and she actually intended for this question to be dropped lol. Thanks so much for your help though, say are you any good at average rate of change though?

Answer 36

Oh okay that explains it then lol. The solution looked really complex. I can take a look at the problem, go ahead and post it.

Answer 37

Two students in your class, Wilson and Alexis, are disputing a function. Wilson says for the function, beween x=-1 and x=1, the average rate of change is 0. Alexis says that for the function, between x=-1 and x=1, the graph goes up through a turning point and then back down. Explain how Wilson and Alexis can both be correct.

Answer 38

Now she said that this is all about finding the slope the y2-y1 over x2-x1. I know how to do that but since there isn't a graph she says I have to work it out without it. That's the tricky part.

Answer 39

Well, if the function has the y values for x=-1 and x=1 equal the same, then the average rate of change must be 0.

For every part of the functionthat goes up between the two, there must be a part that goes down an equal amount, so the overall rate of change would be 0.

Answer 40

So if the graph looks like, say, -x^2 +4

Answer 41

The graph would go up from x=-1, turn around, and end up at the starting point at x=1

and have an overall rate of change = 0

Answer 42

Okay gimme one second.

Answer 43

You can just draw any generic upside down parabola and it be correct, so long as the starting y position is the same as the end.

Answer 44

Cause if y2 = y1, then y2-y1 divided by anything would = 0

Answer 45

Okay that makes sense. Thank you:))

Answer 46

No problem.

Answer 47

You up for one more?

Answer 48

Go ahead

Answer 49

Thanks! Your friend hands you a graph of the performance statistics of the newest car to roll off the assembly line. He says, "I know this is translated graph of either x^3 or x^4, but I can't figure out which one. Use complete sentences, explain to your friend how to tell if it is an even or odd function and how to determine the amount the graph has been translated.

Answer 50

Okay, so an x^4 graph looks pretty much exactly like an x^2 graph (except steeper on both sides). This is because any number to the 4th power will end up positive. -1 x -1 x -1 x-1 = 1. This is true of any even numbered function. You can essentially break it down in to sets:

(-1x-1) x (-1x-1). Each set of two will always give a positive number, so if there's an even number of numbers, it'll always be positive.

Answer 51

An odd function will look like a sideways s, cause there's one "extra" negative number with each set. For example, with three it'll be

(-1x-1) x (-1 x-1) x -1

So any odd powered function will be that sideways s because it'll go to negative infinity on one side

Answer 52

So simply look at the shape of the graph, and depending if it looks like one or the other you'll know if its odd or even (and from that, if its x^3 translated or x^4 translated).

Answer 53

ok gimme one second. I have to read understand it so I can put it in my own words. Lol... thank you so much tho, you've been more than the best help I've got all day! :D

Answer 54

Its no problem. ^.^

Answer 55

One last thing: What shape or what does x^4 look like? Like what shape does it take?

Answer 56

So, all even numbered functions look about the same. Plugging in a negative number will give you a postive one, and plugging in lower and lower negative numbers, of higher and higher postive ones, will have it growing expoentially on either side.

So it'll look just like a x^2 graph. A parabola. Basically a big U if its positive. Except it'll be steeper on either side since its to the 4th power and as such going to rise faster.

Answer 57

Ah I understand. Well I'm finally finished, thank you so much :) Have a good weekend and Winter :D