This problem covers the basics of graphing polynomials. All the essentials to graphing them include end behavior, x-intercepts with multiplicities, y-intercepts, the equation itself, the factored equation, and of course, the graph. We graphed end behavior, but that was step 1. By graphing the information in the middle, we can move on to the next level, which is precisely what this problem is all about: graphing polynomials (without increase and decrease notation as well as minimum and maximum).
There are many things to be aware of. First of all, know the multiplicities, and have the knowledge of what it means to go through a point, to bounce off a point, and to curve through a point. The names are literally what they mean. Make sure to have the write end behavior (even positive, etc.) or your graph will become incorrect. Even positive or even negative should be the focus on these student problems, and arrows should be drawn preemptively to ensure maximum clarity.
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