“Punctuation is the art of dividing a written composition into sentences, or parts of sentences, by points or stops, for the purpose of marking the different pauses which the sense, and an accurate pronunciation, require.”
— Lindley Murray —

QUESTION MARK

A mark indicating a question.
Seriously.

Use a question mark only after a direct question.
Will you go with me?
I asked if he would go with me.

Use a question mark when a sentence is half statement and half question.
You do care, don’t you?

— The Blue Book of Grammar and Punctuation —

PLACEMENT WITH QUOTATION MARKS: Put a question mark within closing quotation marks when the punctuation applies to the quotation itself and outside when it applies to the whole sentence.
His wife asked, “Did you walk the dog?”
Who wrote “The Star Spangled Banner”?

— Owl On-Line Writing Lab —
— The Associated Press Stylebook —