How do you derive an equation if you know the asymptotes? I am trying to curve fit and let's say you have a data set in which you know the asymptotes are:
$y = 0$
$y = -x + 683$
The data always has a positive $x$ value, and the data converges to the line $y = -x + 683$ and has a parabola looking shape.  The data is on the right side of the line $y = -x + 683$.
How do I back into an equation with these asymptotes?  Is there a pattern or math trick/relationship that will allow me to derive curves in the future if I know the asymptotes?
Obviously I don't know how curved the curvature of the line is, but is there a general equation that I have and then I can use R to find the curvature?  This question is similar to this one: Finding family of curve for given asymptotes

A simple function that shoul make the work is the following
$$f(x)=-x+683+\frac{k}{x^a}$$
with $k,a>0$ parameters to fit the data.
