To determine the value of a 1776-1976 Bicentennial Quarter, visit the Price Guide for Beginners page on the Coins section of HA.com. These quarters tend to be worth their face value, as of May 2015.
Visit the HA.com home page, and place the cursor over Departments. On the drop-down menu that appears, click on Coins, Currency & Stamps. Select U.S. Coins from the subsequent menu options. Click View Value Guides under the Value Your Item heading, and choose Coins for Beginners from the drop-down menu. Click on Bicentennial Coinage for information about those coins, or scroll down to Washington Quarters Bicentennial (Dated 1776-1976) for pricing information.
In 1970, the U.S. American Revolution Bicentennial Commission came up with the idea of making special coins in honor of the nation's bicentennial. On July 24, 1973, the House Committee on Banking and Currency proposed the creation of commemorative quarters, half-dollars and dollar coins. An open design competition began to choose the design for the back side of the coins. Contestants submitted about 900 designs. After three months, the committee chose the Revolutionary drummer boy designed by Jack L. Ahr for the quarter.
The government minted hundreds of millions of Bicentennial Quarters between 1975 and 1976. Because of the large amount in circulation, these quarters have no added value.