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

This picture will show you how to find the end behavior as well as the x intercepts and multiplicities. You will also learn how to tell if the graph will go "Thru", "Bounce", or "Curve". The picture shows the basic steps of how to sketch a graph based on multiplicities and x intercepts.

The first step to solve this equation is to factor out the equation. Once you have done that, the answer should be: (x-2)(x-2)(x+2)(x+1). As you can tell from the equation, it is even positive. This means that both the end points go upwards. To find the x intercepts, you put each factor equal to zero. The answers should be: (2,0) M2, (-2,0) M1, (-1,0) M1. Next, you find the y intercept is 8 because you substitute all the X's for 0's; the answer should be: (0,8). To graph it, you look at the multiplicities if it's a multiplicity of one, then it's through. If it's a multiplicity of 2, then the graph bounces and if it's a multiplicity of 3, it's curving.