# How do you describe the end behavior of #y= x^4-4x^2#?

##### 1 Answer

Well, the end behavior can be found by the degree of the polynomial and the sign of the first term.

The degree for this polynomial is 4 because

The sign of this term is positive.

To understand end behaviors, there are 4 possibilities

Odd degree, positive

Odd degree, negative

Even degree, positive

Even degree, negative

This equation is clearly even, positive.

Now, the best way to think of their end behaviors is to think about parent functions

odd, positive =

odd, negative =

even, positive =

Even, negative =

Therefore, this equation has arrows pointing in quadrants 2 and 1.

Remember: Just picture the graph for the parent functions above and you will understand end behaviors much more clearly.