function P(x) = x4 − x3 − 11x2 + 9x + 18. 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). (10 points)
1 answer:
4th degree, so the ends both point in same direction
positive leading coefient so both ends point up
factor it to see wheere the roots are
the roots are r1,r2,r3,r4 in P(x)=(x-r1)(x-r2)(x-r3)(x-r4)
factor
P(x)=(x-3)(x-2)(x+1)(x+3)
the roots are
3,2,-1,-3
disregard negative roots becasue you can't have negative time or something
3 or 2
see my rough graph
here is rough scetch
positive leading coefient so both ends point up
factor it to see wheere the roots are
the roots are r1,r2,r3,r4 in P(x)=(x-r1)(x-r2)(x-r3)(x-r4)
factor
P(x)=(x-3)(x-2)(x+1)(x+3)
the roots are
3,2,-1,-3
disregard negative roots becasue you can't have negative time or something
3 or 2
see my rough graph
here is rough scetch
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All of the sides are the same length.