# Using the Leading coefficient test to determine the end behavior of a polynomial

Brian McLogan
Published at : 08 Jan 2021
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Learn how to determine the end behavior of the graph of a polynomial function. To do this we will first need to make sure we have the polynomial in standard form with descending powers. We will then identify the leading terms so that we can identify the leading coefficient and degree of the polynomial.

The end behavior of a polynomial depends on the leading coefficient (the coefficient of the term with the greatest power) and the degree (the exponent of the term with the greatest power) of the polynomial. If the degree is even and the leading coefficient is positive, the graph of the polynomial rises left and rises right. If the degee is even and the leading coefficient is negative, the graph of the polynomial falls left and falls right. If the degee is odd and the leading coefficient is positive, the graph of the polynomial falls left and rises right. If the degee is odd and the leading coefficient is negative, the graph of the polynomial rises left and falls right.
#polynomials #endbehavior
#polynomials #endbehavior