Do I need to include a squared and linear variable in a random forest to achieve a parabolic effect? I'm using a random forest model. One of my independent variables almost certainly has a parabolic effect on the dependent variable. In a linear regression, I would include the variable as both linear and squared in order to capture this effect. Should I do the same in a random forest?

By extension, same question for variables that have logistic effects (age, for example)?
Random Forest uses a ensemble of Decision Trees using CART algorithm.

Since CARTs (Classification And Regression Tree) are a non-parametric algorithm, they should be able to find interactions between variables and non-linear behaviors.

Nevertheless, building polynomials can help them have a better performance.