Multiplicity

Last week we started our study of Polynomial Functions in Pre-Cal with a discussion of end behavior, followed up with this worksheet to check for understanding.  So now that we know what the ends of the graph are doing, we move to what happens in the middle, or what I call "the wiggle".  I think I'm going to use a combination of these two activities, but I'm not sure yet what order I'll do them in.  I'm thinking I'll use the first one to introduce the concept of zeros and multiplicity and then do the second one to reinforce.  I've taken a completely different approach to this topic this year - I haven't ever been happy with the way the book teaches polynomials - and I'm hoping that this approach will help my students see the "big picture" instead of just teaching them a bunch of seemingly unrelated topics and processes.