math

PLease help!
anyy would be appreciated !thx

what is an example of a quadratic function that touches its axis and also its reciprocal?

-discuss about the vertical asymptotes of the reciprocal an why they occur?

-what can we say about the vertex of the quadratic and corresponding feature of the reciprocal?


asked by jackk
  1. What do you mean by "touching its axis?" Intersecting the y axis? the x axis? The axes are not properties of the function. Then you say "touching its reciprocal" do you mean the function equals its reciprocal somewhere?

    Consider the function
    y = (x-1)^2 -1 = x^2 -2x
    It crosses the y axis (x=0) at y = 0
    It crosses the x axis (y=0) at x=0 and x=2
    The reciprocal is 1/[x(x-2)].
    The function equals the reciprocal at
    [x(x-2)]^2 = 1
    x(x-2)= +1 or -1
    x = 1, 1 + sqrt2

    The function has a "vertex" minimum at x=1 and the reciprocal has a maximum there

    posted by drwls

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