Question

You are having a conference call with the CEO of a paper company. You have interpreted the number of trees cut down versus profit as the function P(x) = –x^4 + x^3 + 7x^2 − x − 6. 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

K, so when x=0, then y=-6
so it goes through the y axis (up and down line) at y=-6

now find the x intercepts, or where y=0
factoring we get P(x)=-1(x+2)(x+1)(x-1)(x-3)
so it goes through the y axis at x=-2, x=-1, x=1, and x=3
put those points
now, the function is 4th degree and the leading coefient is negative, so it starts from bottom left and ends at bottom right
so draw a graph starting from bottom left and going through those points and ending at bottom right
since they are all odd multiplicities, the graph goes through the points to the other side of x axis instead of bouncing off

see graph included (hand drawn)