For example 2x^3/x-1, when you divide 2x^3 by x-1 you will get a quadratic function, when you graph that function, that will be the quadratic asymptote.
A quadratic asymptote is an asymptote on a rational function which looks like a parabola. So if you are graphing a rational function with a quadratic asymptote is doesn't pass through. Just like the oblique, vertical and horizontal asymptotes.
im not really sure, but we have to figure it out. Its like vertical, horizontal and oblique asymptotes in rational function. I have to figure out if there could be a cubic asymptote. I know that there could be a quadratic asymptote, but I am not sure about cubic.