SP #2: Unit E Concept 7: Graphing a Polynomial and Identifying All Key Parts

 This Is the Problem and the Factored equation is also listed. Make sure to please solve this yourself before actually checking the answers.

 This is the final graph of the equation.

My equation for This SP is f(x)=x^4-5x^3-4x^2+44x-48

 This problem demonstrates how to find the end behavior of each graph and their x-intercepts. The ending behaviors is solved by just looking at the equation itself. The entire point of this studenjt problem is to be able to solve the ending behaviour and to be able to plot the x-intercepts on the graph and connect them in a way that will make this all work out. For this End behaviou problem we will not need to find the extrema. Which means we do not need a calculator for this problem. Pay close attention as to how the line ofn the graphs and the points are connected.

There are many things that we must look out for in order to be able to solve this equation. In order to be able to find the factored equation you must factor out any common factors of the equation. If there aren't any then we shall go straight to using the X and factoring out. Once we have done this we must find the end behavior. Since our highest degree is even and the leading coefficient is positive the graph will be As (x) approaches infinity f(x) is positive infinity and as (x) approaches negative infinity f(x) is positive infinity. Both ends of the graph are going up.  The X-intercepts are (2,0) M2 (-3,0) M1 and (4,0) M1. The multiplicity determines if the line will end up going Through (M1), Bounce(M2), or Curve(M3). To find the y-intercept you plug in 0 into x and that will be your answer.