@Mary Lloyd
It sounds like your parents are purchasing a property and using that property as a Primary residence and that you are just being listed on the deed as a partial owner. That you do not have any financial stake in the property. That you are not putting out down payment money or signing loan docs. If that is the case then Mom and Dad claim it as a Primary and you don't claim anything.
If you are securing the debt on the property making loan payments and the such then it would fall into the realm of a second property. You would have to speak with your CPA to discuss exactly what your tax burden would be and the best way to go about mitigating that burden.
Lastly you don't have to be on the deed to run the show, meaning Mom and Dad can buy the property live there then move and rent the property out using you to run the entire operation of renting the place out. They would be the owners and you would act in the role of the property manager.
Being listed on the deed in my opinion is a good idea from the stand point of if anything were to happen to your parents you are listed as an owner and this will help with any probate affairs they may arise. That's a legal item and needs to be confirmed with your attorney, but that is my understanding of it.