Math Problems

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Pc 2-1/2.2 Intro into zeros of a function

Since I am not in class today I am going to provide you with some videos that will help you with your understanding of the content.  The first  two videos are a review of what we completed the first day in this chapter.  Learning how to determine if a function is a polynomial or not and determining the degree and leading coefficient.  Watch these videos if you start having trouble with your homework by determining the end behavior of a function.

Determine if a function is a polynomial or not

Determine the degree and leading coefficient of a polynomial

Now let’s get started on your homework. To complete the following problems you will first need to remember transformations and how they affect a graph. The video below reviews transformations of the 12 basic functions but you will only need to describe the transformations of different polynomials. pg 193 1-6

Transformations of functions

The next type of problems I will expect you to complete will ask you how to write the end behavior of a polynomial using the leading coefficient test. To apply this test you have to know how to write a polynomial in descending power form(standard form) as well as identify the leading coefficient and degree. If you are having trouble with that please review the second video of this post. Do not graph the functions as the directions from the book tell you. Only graph to check your answer pg 193 17-24

Determine the end behavior of a polynomial

For the next set of problems we will learn how to find the zeros of a function algebraically. We will do this by factoring. Remember the zeros of a polynomial are the values that make f(x)=0. Therefore the first step you will take will be replace f(x) with 0. Then you will need to factor the polynomial and solve for that values of x that make the equation true. pg 193 29-32

Find the zeros of a polynomial by factoring

Once you know how to find the zeros we have to understand how to find the multiplicity of each zero. As noted in your Focus Lesson. When you are have a polynomial factored, the factors (x+c)^m have a multiplicity of m . Which is the power of each factor. In the video below I show you how to find the multiplicity from a factored polynomial for each zero. This corresponds to problems pg 193 39-42

Find the multiplicity of a polynomial in factored form

Lastly you will need to know how to to write the equation of a polynomial when given a set of zeros. The process for this is basically the same as finding the zeros of a polynomial by factoring but backwards.
pg 194 53-52
ex) zeros 3,-2

    1. Set each zero equal to x, ex) x=3,x=-2
    2. Set x and your zero on the same side, to equal zero ex) x-3=0, x+2=0
    3. These are your factors multiply them ex) (x-3)(x+2)=0
    4. Replace 0 with f(x) ex) f(x)=(x-3)(x+2)
    5. Multiply out factors f(x)=x^2-x-6

Writing the equation of a polynomial given rational zeros

Writing the equation of a polynomial given irrational zeros

 

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