car died

today i went to go get some dinner and drove my car about 15 mins away to go eat and by the time i came back out about 45 mins maybe my car was dead, the openers didnt work no power no nothing, tried turning it on, nothing at all just a turn of the key with no clicking nothing. Got a jump start and jumped my car it started right up then. took battery to murrays and said the battery is good just was low on charge, so he charged it, seems to be starting good now.....think it might be the alternator? Its started fine every time ive gone out to start it now for past about 3 hours. Its outside running right now for about 10-15 mins now with music, a/c, headlights on and doing fine, any suggestions?

what would be the proper way to test it? I am assuming take it off and over to murrays and have them test it, am i correct? they cant test it on the vehicle i would think.

ill check underneath it tomorrow once i get off work, it seems to be running fine now though. Drove it around for a hour let it sit about 45 mins then it fired right back up with no problems. Odd i tell ya. thanks for the reply