Finding the simplest equation for this curve shape

Question

This is the rough spline that I'm trying to find the simplest equation for.
The only data point constrains are {0,0} and {1024,256}

The closest I've got is this:
How can I go about refining the equation so that it intersects the two points?
Or is there a better / simpler way of doing this other than with tanh?

Thanks!

Answer 1

viable solution found: $\frac{x-512}{128+|x-512|}$*160+128

(thanks to Joel Reyes Noche!)

Answer 2

If you are comfortable with differential equations set up a convenient ordinary differential equation of an odd function with unity as slope ( or as desired) at $x=0,y=0 $ and slope tending asymptotically to zero as $ x \rightarrow \pm \infty.$