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# Rational Function

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Howdy, been spending a lot of time trying to figure this one out.

The equation of an asymptote can be a constant, which makes it a horizontal asymptote. An asymptote can also be linear, which makes it an oblique asymptote. But asymptotes can have even higher degrees. For example, an asymptote that is quadratic is called a parabolic asymptote.

Find the equation of the parabolic asymptote of the graph of

y= (2x+4-3)/(x^2-4x+1)

Thank you.  Any help would be helpful

May 24, 2024

#1
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Do you mean                     ( 2x^4 -3)

y =          ____________         ????

(x^2 - 4x + 1)

May 24, 2024
#2
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Yes I'm sorry.  This is my first time using this platform.  Ain't sure how to format things.

#3
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No problem

Just some polynomial division

x^2  + 4x  + 15

x^2 - 4x + 1   [  x^4  + 0x^3 + 0x^2 + 0x - 3 ]

x^4 -  4x^3  + 1x^2

___________________

4x^3 - 1x^2 + 0x

4x^3 -16x^2 + 4x

________________

15x^2  - 4x - 3

15x^2 - 60x +15

______________

56x - 18        (this remainder is  ignored)

The parabolis asymtote is    y =   x^2 + 4x + 15

CPhill  May 24, 2024