In section 2 of Being and Time, Heidegger discusses "what belongs to a question in general". In particular, he writes (transl. by Joan Stambaugh)
Every questioning is a seeking. Every seeking takes its direction beforehand from what is sought. Questioning is a knowing search for beings in their thatness and whatness. The knowing search can become an "investigation," as the revealing determination of what the question aims at. As questioning about ... questioning has what it asks about [Befragtes]. All asking about ... is in some way an inquiring of ... . Besides what is asked, what is interrogated [Gefragtes] also belongs to questioning. What is questioned is to be defined and conceptualized in the investigating, that is, the specifically theoretical, question. As what is really intended, what is to be ascertained [Erfragtes] lies in what is questioned; here questioning arrives at its goal.
I think this is a great passage. I am also wondering: is this threefold structuring of the act of questioning an original idea by Heidegger, or is he taking his cue from some earlier thinker(s), for example from medieval philosophy? (Somehow, to me, the threefold partition has a medieval ring about it.)
Edit: in his book Making Sense of Heidegger, Thomas Sheehan discusses the threefold structure quite extensively (starting on p. 13), calling it "the three moments of any question". He claims that the Befragtes is "what medieval Scholasticism called the obiectum materiale quod or material object". Other than that, though, he does not give any indication that any writers before Heidegger have adopted the same threefold subdivision.