(1) This problem will go over how to graph a polynomial and find the characteristics stated in the above title. In this particular problem, we will be using the quartic polynomial x^4 - 4x^3 - 12x^2. In order to complete the problem, we will be going through a number of steps, including factoring the polynomial, finding end behavior, solving for the x and y intercepts, calculating extrema and intervals of increase/decrease, and of course graphing.
(2)The reader must pay attention to detail for a little mistake could ruin the entire graph. Also, one thing the reader must be attentive to is the set window when plugging the polynomial into a graphing calculator to graph. This is because the problem results in large numbers and as a result the graph does not fit into the standard zoom.