Is there a simple equation ($y=f(x)$) that can give me the general shape of a black body curve?
Here's an image by Brews ohare to show you what I mean:
Is there a polynomial equation that can give a similar shape? It would be nice to have the horizontal asymptote at $y=0$, but isn't necessarily required if it would simplify the equation.
It sounds like you are looking for Planck's Law.