Question

how do i find the slant asymptotes of y=-2x^2+5x+1/x-2?

Answer 1

Here's a 20 min video on this type of probem

http://www.khanacademy.org/math/algebra/ck12-algebra-1/v/asymptotes-of-rational-functions

I assume the problem is
\[ y= \frac{-2^2+5x+1}{x-2} \]
(You should parens in to make it clear what you mean:
y= (-2x^2+5x+1)/(x-2)

asymptotes are lines that the curve approaches, but does not reach.
Do you see any values that x cannot take?

Answer 2

x cannot equal 2?

Answer 3

as x gets close to 2, the denominator approaches zero. Dividing by a small number gives a big number. so y approaches positive infinity when x approaches 2 from the left.
x=2 is one of your asymptotes

Divide x-2 into the numerator to find the other