"Have you remembered your father's birthday?"
Translation:Ti sei ricordato del compleanno di tuo padre?
Ricordare means to Remember or to Remind. There is obviously ambiguity with this verb. A transitive sentence such as "I remember the birthday of my father " would use avere as the auxiliary verb. If you alter the sentence to "I remind myself of the birthday of my father, the sentence becomes reflexive and essere is needed as an auxiliary verb. Another example would be "I remembered yesterday" .. Mi sono ricordato ieri.
Maybe I'm being too generous with "possible translations," but couldn't "your" in English translate to "vostro," even if the "You" in the Italian sentence appears in the singular? Speaking to a son or daughter who has siblings, it wouldn't be totally illogical to ask one person ("tu"), "Did you remember your (plural; "vostro") father's birthday." Would it?
My Italian isn't great, but the language is similar enough to French (my native language) for me to answer this. Technically, yes, you could say vostro, but it sounds really weird and would imply that you are talking to more than one person at a time and pointedly asking one sibling in an accusatory tone. So that would be a sentence structure that would almost never be used.
In Italian the pronoun can be implied.
"Ricordare" is often used as a reflexive verb, "ricordarsi" it means it should be used as follows
(Io) mi ricordo di qualcosa
(Tu) ti ricordi di qualcosa
(Lui) si ricorda di qualcosa
(Noi) ci ricordiamo di qualcosa
(Voi) vi ricordate di qualcosa
(Loro) si ricordano di qualcosa
Another possible translation would be "Hai ricordato il compleanno di tuo padre?" (In this case, "ricordare" is not reflexive)
I think that the translation given by Duo is the most common.