You have the MacBookPro6,2—the Edsel of Macs. It may have the logic-board defect that was covered by a recall program that has now ended.
The model was discontinued in February 2011. As of five years from that date, it will be classified by Apple as a "vintage product." That means Apple will most likely refuse to service it (but see the exceptions on the linked page.) In that case, you would have to go to an independent service provider. The part may no longer be available, or the repair may not be cost-effective.
Make a "Genius" appointment at an Apple Store, or go to another authorized service provider, to have the machine tested. The routine hardware diagnostics used by service providers do not detect the fault. There is a specific test for this issue that Apple calls "VST" (for "Video System Test.") Ask for it. A "Failed" result means that the fault is present.
You may be quoted a price of about $350 (in the U.S.) for a "depot repair," which involves shipping the unit to a central repair facility and takes about two weeks. For that flat fee, anything found wrong with it should be fixed, not just the logic board.
Sometimes the replacement part is also defective, so be prepared for that possibility. If you decide to pay for a new logic board, test thoroughly during the 90-day warranty period on the repair. Some owners have reported that they went through as many as three replacement boards before getting one that worked.
If you don't want to pay for the repair, you may (or may not) be able to work around the problem by disabling automatic graphics switching. To use the discrete graphics processor, you'll need a third-party utility to switch to it manually.
Often the problems start after an OS upgrade. If the upgrade was recent, and you have backups, then you can revert to a previous OS X version.
