"Are your parents doctors?"
Translation:I tuoi genitori sono dottori?
At least in the lessons I've done so far, Duolingo seems to ignore the existence of the formal you completely (as well as the super-literary-formal use of voi for singular-you.) On the whole this is probably a good thing - yeah, once or twice I've tried to use the formal you intentionally and gotten told by duolingo that i'm wrong, but more ofen when I do that I've just plain made a mistake.
And to specifically answer your question, yes, if you were talking to someone you just met in and not among young people, you would probably use suoi here.