1) Y= X1+ X1*X1+X2 + X1*X2 + (X2)*(X1*X1) i.e. adding not only the interaction with the low level X1 but also the interaction with the quadratic term X1*X1.
2) Y= X1+ X1*X1+X2 + X1*X2 i.e. just adding the interaction between X2 and the lower level of X1.

x1 is a continuous var the child's health whereas x2 is gender.
y is a dummy variable so this is a probit model.
im actually trying to capture non linear relationship and would it be necessary to include "the quadratic term interacted with the gender variable"
what if i dont?

and yes im using factor variables