Sketch the graph of polynomial function P(x)=15x(x−5)2 make sure the graph shows all intercepts and exhibits the proper end behaviour.
The function has an odd degree 3 and a positive leading coefficient. Thus, its end behaviour is y→−∞ as x→−∞ and y→∞ as x→∞.
To solve for the x-intercept, we set y=0.
0=15x(x−5)20=xand(x−5)2=0
We have,
x=0 and x=5
To solve for the y-intercept, we set x=0
y=15(0)(0−5)2=0
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