# POLQ 3 | Lesson 3 | Explore (Leading Coefficient) Leading Coefficient Test

Now that we know how zeros affect a polynomial graph, the next step is to figure out the end behavior.

The first term, $$a_n x^n$$, of a polynomial provides end behavior information.

First Term of the Polynomial End Behavior of Graph
When $$n$$ is even and $$a_n$$ is positive The graph appears from the top left of the coordinate plane and leaves at the top right.
Graph rises to the left and right.
When $$n$$ is even and $$a_n$$ is negative Ends of the graph appears from the bottom left of the coordinate plane and leaves at bottom right.
Graph falls to the left and right.
When $$n$$ is odd and $$a_n$$ is positive The graph appears from the bottom left of the coordinate plane and leaves at the top right.
Graph falls to the left and rises to the right.
When $$n$$ is odd and $$a_n$$ is negative The graph appears from the top left of the coordinate plane and leaves at the bottom right.
Graph falls to the right and rises to the left.