Sorry, but we would need more information about what you say about "working well".
What are you going to use your computer for? And what you mean by "Can the graphic card run well"?
If the card isn't broken, it will always work "well" if it simply works, if you are trying to play games on that graphic card, sure that some games won't be playable at High settings and At High resolutions.
If it is too laggy problem, simply buy a new card like the 6670 or the 6750 etc...