SOLUTION: f(x)= -2x(x-5)(x+1)(x-2)^2 X and Y intercepts The end behavior of the graph

Algebra ->  Systems-of-equations -> SOLUTION: f(x)= -2x(x-5)(x+1)(x-2)^2 X and Y intercepts The end behavior of the graph      Log On


   

Question 351563: f(x)= -2x(x-5)(x+1)(x-2)^2
X and Y intercepts
The end behavior of the graph
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-intercept, set y=0 and solve for x.
f(x)=0
By the zero product property, there are 3 x-intercepts.
highlight%28x=0%29
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x-5=0
highlight%28x=5%29
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x-2=0
highlight%28x=2%29
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To find the y-intercept, set x=0 and solve for y.
f%280%29=+-2%280%29%280-5%29%280%2B1%29%28x-2%29%5E2
highlight_green%28f%280%29=0%29
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f(x)= -2x(x-5)(x+1)(x-2)^2
When x has a very large positive value,
f(x)=-(+)(+)(+)(+)^2=-
Then f(x) has a very large negative value.
lim%28x-%3Einfinity%2C+f%28x%29=-infinity%29
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When x has a very large negative value,
f(x)=-(-)(-)(-)(-)^2=+
Then f(x) has a very large positive value.
lim%28x-%3E-infinity%2C+f%28x%29=infinity%29
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