Sketch the graph of polynomial function P(x)=(x−1)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=(0−3)2(0+1)2y=(3)2(1)2y=9
To solve for the x-intercept, we set y=0
0=(x−3)2(x+1)2
By zero product property, we have
(x−3)2 and (x+1)2=0
x=3 and x=−1
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