Can I upgrade the graphics on this machine?

Short answer: yes...ish.

These should be the specs on the computer:

http://www.shopping.hp.com/product [...] AA%2523ABA

However, they don't list the PSU. You do have a free PCI-E x16, so you can put a new card in, but if the PSU is feeble like in most prebuilts (it is sized to what the base system needs, so if you add something power hungry...) you will need to upgrade it. That still is no huge deal, as a PSU upgrade is only $50 or so, but that is a bit more work than just plopping a new card in.

according to this thread from a couple days ago, that computer comes with a 300W power supply, which is pretty puny. But likely enough to support some of the cards with lower power consumption, like an HD4650 or HD4670 (I've got the former in my old machine with a 350W supply).

http://www.tomshardware.com/forum/ [...] ion-p6240f

Lol @ "Out of Stock" in big red letters. At any rate, you should obtain at least a 450W power supply to go with it, I'd recommend overshooting the minimum a bit and getting a 550W. The good cards availible at retail stores (ATI 4850, GeForce GTX260) require a 450W minimum, and retail computers (even gaming ones) pinch pennies in areas you wouldn't think of. Even ASUS gaming machines at Best Buy have power supplies only large enough to cover what's in the computer already, not to cover future upgrades or add-ons.

Or maybe dont save money, but get better components as big system builders usually use lower quality and cheaper brands to save money.

There are no free lunches.