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How do you find the chromatic number?
There are many ways to find the chromatic number. One way is to write the chromatic polynomial and obtain it from that. For example, let's look at a complete graph on 3 points which looks like a triangle. We can color the first vertex in x ways, the second is x-1 ways and the third in x-2 ways. So the chromatic polynomial is C(x)=x(x-1)(x-2) not the smallest natural number, N, such that C(N) is not equal to zero is the chromatic number. So in this case it is 3. This number tells us the we can color the graph with 3 different colors and have no vertices with the same color. Any smaller number of colors, say 2 would not work.So the answer is find C(x) the chromatic polynomial and then find the smallest natural number such that C(x) is not zero. There are many other methods to find it, but that one is sometimes the simplest.
What can the degree of a polynomial tell you about the graph?
The degree is equal to the maximum number of times the graph can cross a horizontal line.
What best describes a root of a polynomial?
A value of the variable when the polynomial has a value of 0. Equivalently, the value of the variable when the graph of the polynomial intersects the variable axis (usually the x-axis).
What is the point at which a graph crosses the x-axis?
For a line, this is the x-intercept. For a polynomial, these points are the roots or solutions of the polynomial at which y=0.
What part of a polynomial function determines the shape and end behavior of a graph?
The order of the polynomial (the highest power) and the coefficient of the highest power.
