I need a function f(x), that uses a as a constant.

-1<a<1

I need:

f(-1)=0

f(1)=1

f(a)=.5

The function must always have a positive (or zero) slope, and I would like it to be as smooth as possible.

I would also like the slope to be highest near a.

It must be continuous and differentiable everywhere from x=-1 to 1. Thanks :D

The function will be used in a computer program, so the most simple solution is best.