This problem is to show my understanding about the multiplicities that are solved for when you factor a polynomial. It also shows the y- intercept as well as the end behavior to help others understand how I am able to graph it. The problem also shows the graph to show what the polynomial would look like if plotted on a graphing calculator.
The viewer needs to pay special attention to the multiplicities and the end behavior. The end behavior helps tell how the end points of the graph and whether it goes up or down. The multiplicities help determine how the graph will pass the x-axis either through bouncing, going through it, or curving. These are some of the things that you, the viewer, should pay attention to when going over this problem.
Steps
1. Factor out the equation by splitting it up.
2. Set each factor equal to zero and solve
3. The solved are known as multiplicities
4. Multiplicities are 3M2, 4M1, and -2M1
5. End behavior show how the endpoints of the graph either go up or down. In this case they go up.
6. The y - intercept is found by plugging in 0 for all of the equations which shows that it is (0,-72)
7. The multiplicities determine how the graph passes the x-axis at the gates.
8. Roughly graph the equation according to multiplicities.
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