SP #2: Unit E Concept 7: Graphing polynomials, including: x-int, y-int, zeroes (with multiplicities) and end behavior

     This problem demonstrates the techniques of graphing a polynomial equation, which includes the end behavior, finding x & y intercepts, and zeroes (multiplicities). The graphs are very similar to Concept 4, except now we have to determined the humps or the way it should be shaped in the middle of the graph. The multiplicities will let us know if we should either go through, bounce, or curve in the graph.

   Make sure to pay close attention to the multiplicities and the end behavior. The multiplicities let us know what is going on in the middle of the graph, while the end behavior tells us what type of graph it is, whether it is an odd-positive, odd-negative, even-positive, or an even-negative graph. Also, make sure to pay attention to the y-intercept. It'll tell you how high the "hump" should go.


Steps and Explanations!! 1. Factor out the equation carefully. 2. Determine the end behavior based on the leading coefficient and degree of the original equation. Make sure to also write your notation based on the type of graph it is! 3. List out your x-intercepts based on what you just factored. Don't forget to include the multiplicities. 4. Find the y-intercept by plugging in zero or "x". 5. Graph! Make sure to use the end behavior and the x & y intercepts to graph!