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math pre calculus

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find the following for the function f(x)=(x+5)^2(x-2)^2
a.find the x and y intercepts,
b.find the power function that the graph ressembles for large values of x c.determine the maximum number of turning points on the graph of f
d.determine the behavior of the graph of f near each x-intercept

I don't even know where to begin. please help.

  • math pre calculus - ,

    surely the intercepts are easy

    f(x) is a polynomial of degree 4, so for large x it just looks like x^4.

    Since the graph just touches the x-axis at x=-5 and 2, It comes down from the upper left, touches at x=-5, goes back up and comes back down to touch at x=2, then heads on up to the right, it has 3 turning points.

    Visit wolframalpha.com and enter

    (x+5)^2(x-2)^2

    to see the graph. It will help clarify the concepts, I think.

    Enter

    plot y=(x+5)^2(x-2)^2 and y=x^4 where -10<x<10

    to see how the two graphs are similar for large x.

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