Friz Quadrata was designed in 1965 by Ernst Friz and Ed Benguiat for Visual Graphic Corp., and released by ITC (International Typeface Corp.) in 1978. The
bold weight was later added by Victor Caruso.
There is no biographical information available about Friz, and this font seems to have been a "one-hit wonder" for him. (Benguiat, however, designed many fonts, including Avant Garde Gothic, Bauhaus, Benguiat, Bookman, Caslon, Korinna and Tiffany.)
The font is not much used in print, and an extensive search in magazines turned up only one example of its use; in a shampoo ad for a product called Redken.
However, a web search revealed numerous uses of Friz Quadrata. For example, a (print) title called The Cigar Book used it for subheads.
Also found were various promotional items inscribed with Friz Quadrata, such as pens and mousepads. The mousepad was a giveaway for a software product called Mercury Scheduling.
Friz Quadrata is also frequently offered as a choice on stationary, monogram and signage products.
Interestingly, the font was also used on clickable buttons on several university web sites.
The font seems to be aimed at a fairly upscale, academic, classically-minded audience.