Bivariate model — non-linear association

Hi All,

I am working on a bivariate model for two continuous variables (normally distributed). 

I have checked the association between these variables and looking at the plots the relationship seems to be non-linear. I have run a regression model and the association is significant but it is probably better explained by a quadratic or U-shaped association. 

My question is about the bivariate model. Would it be biassed? Is there any way to model these non-linear associations in a twin model? What would be the best approach for this scenario?

Thank you so much in advance.