Frank Zappa was a funky musician who was known for playing many different musical genres from rock music, to jazz, to pop, to even classical. That might make you think he was a drug user, like many rock musicians, but in fact he wasn't very keen on drug use after some bad experiences with marijuana. He was a big freedom of speech advocate, which is one of his lasting legacies beyond his music.
In this family photo with his parents, you can see his love for being funky. The room is almost entirely purple. Not only that, both he and his parents are matching with their outfits. By the looks of this picture, it is safe to say that his parents were supportive of all his funky endeavors. Either that or he forced them to take this photo.