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algebra

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find the following for the function
f(x)= (x+5)^2(x-1)^2
a) find the x and y intercepts for the polynomial function f
b) determine whether the graph of f crosses or touches the x axis at each x intercept
C) put all information together to obtain the graph of f

  • algebra -

    The x-intercepts are the roots.
    The y-intercept is at 5^2*1^2 = 25

    Since the roots are of even order, the graph touches the axis at each root.

    So, degree-4 polynomial with positive coefficient. Down from the left, tangent at each root, then back up to the right.

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