Coefficient interpretation in quantile regression

[eviewsuser2015]

Hi,

I am trying to estimate the effect of a company's size on certain aspects of its performance (like returns, costs etc) and have a panel of 3*100 observations. I want to run a quantile regression, because:
a) There are outliers (some very large caompanies)
b) I want to know the effect of a size increase for different size classes

I measure the equation: Y = a + B1*size + B2(size-mean size)^2 + e to allow for higher order effects (I expect the relationship is not monotonous) where the squared term represents the difference between the company's size and the sample (geometrical) mean.
When using this equation in different quantiles, how can I interpret the squared term? Does it still measure the difference between the sample mean, or only the mean of the observations in that quantile?