On modern vehicles there is always some parasitic draw when the car is off, although it should be minimal. First thing I would do is a visual inspection of the battery, the cables, the alternator and the belt. Look to see if the sides of the battery are bulged out, and that it is full of electrolyte if you can. Make sure the cables are free of corrosion, and not just on the terminals but that the cables themselves don't have any inside the wire strands.
What is the voltage output of the alternator, and how was it tested? When testing the alternator turn the headlights on and any other high draw items like windshield wipers, stereo, etc, and see if the voltage drops below 12.5v with the engine revved up around 1k rpm. A good alternator should maintain 13-14.5 volts even under full load if it's much below the 13v it's marginal. I've had voltage regulators go bad and they let the alternator overcharge (output more than 14.5 volts) which will quickly destroy a battery. If everything checks out it is possible you got a bad battery, and you should take it back to where you purchased it for a replacement.