Intel HD Graphics is not an on-board or dedicated graphics card, it's part of the processor (integrated Graphics Processing Unit). It will display resolutions at 1024 x 768 and well above depending on the processor (and by extension the iGPU) but may require an external monitor to display those resolutions. That said, most 15.4" laptops have a minimum resolution of 1366 x 768, you will find laptops with smaller sceeens that support that resolution. It is capable of Direct X 11 and by extension direct X 9 thanks to backward compatibility. It is capable of low end gaming and the newer chips are more powerful so will probably be capable of something mid level gaming. At least the desktop chips are, I'm not so sure about the laptop...