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Describe an effective strategy to use for graphing a polynomial function....

Question

Describe an effective strategy to use for graphing a polynomial function.

Describe an effective strategy to use for graphing a polynomial function.



Answers

For each graph, describe a polynomial function that could represent the graph. (Indicate the degree of the function and the sign of its leading coefficient.)

Hi guys. So today we're solving the question. If a polynomial functions and factor form, what would be a good first step in or determine a degree with function. So let's say we have Home X plus three um, X minus five. You can see that it's already factored. And for us to find the degree who would just equate Thesis zero X equals? Oh, explodes three goes to zero, which is give us actually called negative three when X plus X minus five equal to zero. Now give us X equals five. So since we find that we have two X intercepts, that would give us that would determine how many degrees the function has, which would be two. All right, Thank you.

So we have a function of flex and this secret too a factor for so I'm gonna call that a one x linus Be one all of it to the power if you want and multiplied by the quantities up to a one x minus b and say it's a m here, P So this is very useful because when we have our plot here and we draw and we try to factor our function you see that at this point right here, we have a multiplicity of one. At this point here, we have in simplicity 02 And at this point here we have a multiplicity or three which corresponds to the powers of a factor for

Okay. What I would do to determine the degree of the function would be if it's a factored form, I would distribute. That would be the first thing I could do. Then on top of distributing. After doing this, I would combine like terms because then you can see in a more simplified way. And then from there you should be able to get X to the third extra. Whatever your degree of axes in your power. And once you can see 12 combined your life terms in your exponents, you can see what the expert is, which tells you that.

And this exercise is just a verbal question that asks, Explain how the factor form of the polynomial helps us in graphing it. So for this question is really two things that we are helped with when we have a factor. Former polynomial Imagine we have something like Why equals X squared minus for this is a very easy example. But if we want to graft this, we could kind of easily see that we're gonna have zeros at X equals two and X equals negative, too. But if this was something more complicated, if we factored it, we would get why equals X minus two times X plus two and being able to factor a polynomial, we could very easily see that our zeros would be at negative two and two. So when we factor a polynomial and we want a graph it, if we have it in this form, it's super easy to see where zeros are. There's also the point that when we factor a polynomial, it helps us to see the multiplicity. So, for example, if we have another function will say why to that equals X minus two times X plus two squared. If this wasn't a factor. It would be a lot harder to see the zeroes. And we also wouldn't be able to see this multiplicity off to right here. Which means that we have that zero at X equals negative, too. A curse twice, right? So here we have a zero at two and negative too, but by factoring and were able to see the multiplicity. So there's really just two parts. A. We can easily see the zeroes and B. We can see the multiplicity, and that's why we should always try and Graff polynomial after we factor.


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