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.

 


Go to Practice (Polynomial Characteristics)