A design specification for the obverse of the Washington commemorative required a portrait of Washington which was to be based on a clay bust by .
Per The Official Red Book: A Guide Book of the Washington and State Quarters, the design competition guidelines specified that the obverse of the coin (under the original competition the coin was going to be a half dollar) was to "bear a head of Washington based on the Houdon bust at Mount Vernon."
That said, the purpose of this article is to focus on the Houdon bust of George Washington. Below is a great video I found regarding the bust.
Any time this bust is mentioned it's noted that it's located at Mt. Vernon. This is true, but the above video mentions it to be typically located at The Donald W. Reynolds Museum and Education Center. To clarify this museum and education center is actually located on the grounds of Mt. Vernon. I've been to this location and have seen the bust in person when both my kids took their 6th grade trips to Washington D.C. I Will be returning again this coming fall with my son's 5th grade class and hope to take some good pictures of the bust for this site.
The bust, itself, came out of the work done by Houdon (pictured right) while fulfilling a commission for the Commonwealth of Virginia, who's desire was to erect a life size statue of George Washington, at the Virginia state capitol rotunda, to honor all that General Washington Had done for the United States of America. Both Thomas Jefferson and Benjamin Franklin, who were, at the time, U.S. ambassadors to France, were asked by Governor of Virgina, Benjamin Harrison (pictured left), to select an artist who was up to the task of creating such an important sculpture. Houdon at the time was well known and was the hands down choice of Thomas Jefferson.
A notable difference between the Houdon bust of George Washington and the image as he appears on the quarter, is that Flanagan added a thick roll of hair above the neck and a peruke (the wig with the pony tail tied in a ribbon) to his likeness of George Washington. When you look at the bust this is not what you see. Instead you see a representation of a hairstyle that was common at the time. Since the bust was created from a life mask, which involved covering Washington's face with plaster, I would imagine that the hair you see on the bust was not actually cast in plaster, but was artistically added to the bust by Houdon. However that is an assumption on my part and a detail which is not critical to this article.
Houdon Bust Video credit: https://vimeo.com/mountvernon
Jean-Antoine Houdon image credit - http://en.wikipedia.org/wiki/Jean-Antoine_Houdon
Gov. Benjamin Harrison image credit - http://en.wikipedia.org/wiki/Benjamin_Harrison_V#Governor_of_Virginia