Question

For the polynomial function y=1/3x^2+x+6, your friend says the end behavior of the graph is down and up. What mistake did your friend make?

Answer 1

The friend's error is in the terminology he uses to describe the end behavior. If I showed you this graph, how would you describe the end behavior?

Answer 2

I would agree with him? It is going down and up at the end. But in the beginning it goes up down up down and then up

Answer 3

Remember to look from left to right:

We only care about the ends, not the crazy stuff that happens in the middle. And you also have to make sure to specify left end behavior (LEB) vs. right end behavior (REB). Otherwise no one knows for sure what you're talking about.