SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

This problem is about being able to sketch a relatively accurate graph when given a polynomial. We are able to get an idea of how the graph should look because after factoring, we are able to find and plot the x-intercepts/zeroes, the y-intercept, as well as identify the end behavior (if the graph goes up when we move left, if it goes down, etc. Also, looking back at the zeroes, we should be able to identify the multiplicity of each point, and determine whether the graph will go through (multiplicity of 1), bounce (multiplicity of 2), or curve (multiplicity of 3). To go a step further and create an even more accurate graph, we would find the extremas (min and max) and the intervals of increase and decrease to determine the behavior in between the end behaviors.

A few things that would make graphing these polynomials easier would be to pay attention to end behavior as well as remember that you are only able to go through the x-axis through a point. If you know how the end behavior looks for each kind of graph (even positive, even negative, odd positive, odd negative), you will know where to start and where to end. Also, knowing that you are only able to go through the x-axis through the points, helps us create an accurate graph with little to no mistakes. A trick to remember to go through the points is to think that the x-axis is a wall. Those points are doors. We cannot walk through walls. See my point? (PUN NOT INTENDED... UNTIL NOW.)