bad

First recorded in 1200–1250; Middle English badde, bad; origin uncertain; perhaps akin to Old English bæddel “hermaphrodite,” bædling “womanish man”

The adjective bad meaning “unpleasant, unattractive, unfavorable, spoiled, etc.,” is the usual form to follow such copulative verbs as sound, smell, look, and taste: After the rainstorm the water tasted bad. The coach says the locker room smells bad. After the copulative verb feel, the adjective badly in reference to physical or emotional states is also used and is standard, although bad is more common in formal writing: I feel bad from overeating. She felt badly about her friend's misfortune.
When the adverbial use is required, badly is standard with all verbs: She reacted badly to the criticism. Bad as an adverb appears mainly in informal contexts: I didn't do too bad on the tests. He wants money so bad it hurts. See also badly, good.

The etymology of bad is obscure, and the word has no relatives in other languages. The Middle English form badde is not clearly attested before 1300. Badde may derive from Old English bæddel, bǽddel “hermaphrodite” and bædling “womanish man.”
Bad off, in standard English now badly off, dates to the first half of the 18th century ( badly off dates to roughly the same time). The colloquialism my bad!, an Americanism, dates from the early 1980s.
Bad in its slang sense “excellent, first-rate” is surprisingly old, first appearing in print in the 1890s. It was then popularized in the 1920s within the jazz scene, and is typically associated with Black English. The slang sense “very tough, formidable” also appeared in the 19th century; it often meant “formidably skilled,” which ties in with the “excellent, first-rate” meaning.