I want to do a logistic regression, with multiple covariates, where at least one of the covariates is two-sided. When I say that a covariate $x_1$ is "two-sided", I mean that values close to the mean of $x_1$ are likely to be in class 0, whereas values far away from the mean of $x_1$, in any direction, are likely to be in class 1. Furthermore, the distribution of $x_1$ may not be symmetrical about the mean (for example, a high value of $x_1$ might be somewhat indicative of class 1, whereas a low value of $x_1$ might be extremely indicative of class 1).
One way to do this is to simply say that the actual covariate I give to the logistic regression is the absolute departure of $x_1$ from the mean. Another way is to create two such departure variables, to account for non-symmetry in the distribution of $x_1$. A third way would be to use polynomials of $x_1$. I'm sure there are other potential ways of doing this.
Is there a common "best practice" for handling this situation?