How do I know if my car battery is bad or if it's the alternator?

My last battery went bad to the point where all the water came out of it when I was driving. So I got it replaced with a used battery i got at a battery shop. My turned on quickly with no problem after that for a few weeks. Then one night I left my lights on and had to jump start it. It lasted a few days but now if... show more My last battery went bad to the point where all the water came out of it when I was driving. So I got it replaced with a used battery i got at a battery shop. My turned on quickly with no problem after that for a few weeks. Then one night I left my lights on and had to jump start it. It lasted a few days but now if I leave it off for a few hours I have to jump start it again. It runs fine and everything works fine while I'm driving. But when I turn it off for a few hours it goes dead again? Could this be my alternator sense it's my 2nd battery? Or could the battery just not be good anymore after it went dead the first time ?
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