Question

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?

Answer 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