How do I know if a graphics card is sufficient for a given external monitor? (Time-sensitive)
According to EveryMac.com, the mid-2012 MacBook Pro can support an external monitor with a resolution of 2560x1600.

This means that your Intel HD Graphics 4000 chip is capable of supporting your monitor.  However, you should be aware that the HD 4000 uses shared memory (meaning it takes up to 1.5GB of RAM from the system).  

Personally, I would upgrade your memory to the maximum amount and again, according to EveryMac.com, you can upgrade it to 16GB of PC3-12800 SO-DIMM Memory.  This will ensure that your integrated graphics chip and the system has enough memory to deliver the best graphics performance it possibly can.

Also, regarding the monitor connection, I would avoid converting DisplayPort to HDMI and just stick with DisplayPort (go mDP to DP).