Sunday, January 20, 2013

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 26

Sketch the graph of polynomial function P(x)=(x1)2(x+2)3 make sure the graph shows all intercepts and exhibits the proper end behaviour.

The function has an even degree of 4 and a positive leading coefficient. Thus, its end behaviour is y as x and y as x.
To solve for the y-intercept, we set y=0.


y=(03)2(0+1)2y=(3)2(1)2y=9


To solve for the x-intercept, we set y=0
0=(x3)2(x+1)2

By zero product property, we have
(x3)2 and (x+1)2=0
x=3 and x=1

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