This problem is about deriving a parent function type equation from a regular trinomials, so that graphing the equation wouldn't be as hard as it would have been had you tried to graph the other way. Basically, it's about finding the values that we deem crucial in graphing polynomials, which include the vertex, x-intercept(s) (if there are any), the y-intercept (if there is one), and the axis of symmetry. Ultimately, it's about going through this infinitude of steps, and arriving at a simpler means.
I think that the reader needs most, to pay special attention to whether or not my writing is intelligible to them or not. However, in all seriousness, though, I think that they need to know that all of the important values that we need, can be calculated simply on a calculator right from the start, without having to go through any of these steps. To each, their own, I guess. Also, it's pretty important that you realize imaginary numbers cannot be graphed regularly, such as regular x-values, on a regular graph.
