As another poster has already said, the GPU is integrated into the CPU.
The mid 2012 model is still being sold, does it still have warranty? If it doesn't, you may be able to request a flat rate repair for less than you'd expect.
As someone else mentioned, you could probably get it repaired by Apple for around $300~. It's not a broken graphics chip. If you see hardware artifacts indicative of graphics problems, you would need a new logic board.