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

In this picture we'll be finding on how to find the end behaviors (describes how a graph acts at the extremes - as we go really far to the left (get closer to negative infinity) or as we go really far to the right (get closer to positive infinity). Remember, because this is what happens in the extremes, this tells us nothing about what is happening in the middle - how many ups and downs there are, how many zeroes there are, etc. We just don't care about it. Polynomial end behavior is quite predictable. It is based on two things: 1)Degree & 2)Leading Coefficient. (SECOND PARAGRAPH) But the main goal here in this picture is to know whether this graph will have to go: thru, bounce, or curve at some point. As you can see my equation is y=x^4-13x^2+36. What we first want to do is factor it out to get (x-3)(x+3)(x+2)(x-2). Next, finding the end behavior. The end behavior is as x-> inf., f(x) -> inf. As x -> -inf., f(x) -> inf. In the same manner, 3M1,-3M1,-2M1,2M1. Finally, the y-intercept should be (0,36) because as you plug in 0 in the x's you get 36.