"Excuse me, is this bank open?"
Translation:Elnézést, ez a bank nyitva van?
The words for open and closed in Hungarian behave as adverbs, not adjectives. So nyitva and zárva can not stand alone as the predicate like an adjective would, and they don't take plural or accusative or other endings. They must modify a verb, and that verb must be present in the sentence, even when it is van or vannak.
Ez a bank új - Is this bank new?
Ezek a bankok újak? - Are these banks new?
Ez a bank nyitva van? and Ezek a bankok nyitva vannak?
Great explanation indeed, but I have to beg to differ a little bit. While what jsiehler writes is generally true, "nyitva" and "zárva" sometimes like to stand on their own. They are special. You can actually say "A bank nyitva" or "Nyitva a bank", etc. Let's say it is incomplete, or idiomatic, but it is perfectly fine.
"Zárva a bank, nem tudunk pénzt váltani" - The bank is closed, we cannot exchange money.
But of course you are more than welcome to always say the "van"/"vannak" after "zárva" and "nyitva".
Now, when negating, that is, when it is not closed or not open, we use "nincs":
"Nincs(enek) nyitva/zárva a bank(ok)".
And, as we know, "nincs" stands for "nem van", so the implicit "van" is always there in this case.
For language enthusiasts, you can search for the plural forms of these words. They can be found in older texts, say, from the 19th century. "Zárvák" was very much used in the past, and, interestingly, without "van".
"A házak ajtajai zárvák." - The doors of the houses are closed.
But this is history, these forms are not used anymore.
Here is some more discussion on the topic: