Looking for a function looking similar to quadratic function but skewed to left I am looking for a function looking similar to quadratic function but skewed to left; something like this:

Just ignore numbers and variables in the figure. I am interested only in the shape of the curve. The top does not have to be flat as in the figure. The point is that it is quadratic skewed to left. But I'm not using it as a probability distribution function. So it does not have to have properties of PDF. Actually, I would prefer not to.
Are there any function of this type?

I sometimes use the Linex loss function when I want an asymmetric parabola:
$$f(x) = e^{ax} - ax - 1$$
for some constant $a$.
