Question

You are having a meeting with the CEO of a soda company. You have interpreted the number of cans of soda produced versus profit as the function P(x) = x4−5x3−20x2+60x+144x4-5x3-20x2+60x+144
Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0)

Answer 1

590x + 144 is the correct answer

Answer 2

The graph for P(x) has the y-intercept is (0,144) and is shaped like a W, with the lines very close together. The graph to P(x)= 0 has the root is (0,0), Y- intercept is (0,0), and solution of y=144. This graph will break the company down because it does not show any profits being made. If anything it shows the profits being lost.