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Basic Polynomial Graphs - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Graphing higher degree polynomial functions can be more complicated than graphing linear and a href="/math/algebra/quadratic-equations-and-functions/graphing-quadratic-equations">quadratic functions. Polynomial graphs can be graphs of functions where the degree of the highest term is greater than one. When we graph polynomials with varying degrees it is easier to identify the end behavior, shape and turning points.

The graphs of some basic polynomials, so for this part we're going to look at the graph of some polynomials and some of these are going to be familiar to you some of them not but we're going to go through the same process just to make sure we understand how we got the basic graphs for all these okay. So right here I have f of x is equal to x okay so you should hopefully recognize this outline but we're going to go through the process just so you see exactly how we get these points. So over here I have a table I have certain values of x and certain values for f of x divide that comes out of it. So if x is negative 2, the same value comes out because f of x is just equal to x so that ends up being negative 2 as well.
All of these values are just going to go in and come out exactly the same. So we end up with negative 1, 0, 1 and 2 okay. These then kind of coordinate correspond to points on the graph okay. So we have negative 2, negative 2 and I'm not going to make my graph exact but just enough so it could give us idea of what exactly is happening. Point a of 2 negative 2, negative 1, negative 1, 0 0, 1 1, 2 2. So we end up with a line slope one passing through the origin. We already knew that from just what we know about lines but going through a process we're able to figure out what this polynomial function looks like.

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