non linear relationship

I am trying to investigate the effect of profitability on firm's cash. I constructed two samples ; one for big firms and second for small firms.

I tried to find the if non liner relationship exists.

for small firms i find

cash = profitability + profitability^2 : both independent variables are negative and significant. is this okay ?? i thought it should be negative for profitability but positive for the square of profitability.

is this okay ? what kind of relationship is this ?

however, for big firms i find that profitability is negative but the square of this independent variable is positive.

your support is always appreciated

Faisal