An adverb is used to modify not only a verb but also an adjective, both in Japanese and in English.
とても良い = very good
(とても and very are adverbs which (almost) exclusively modify an adjective)
酷くまずい = terribly yucky
(酷く and terribly are "adverbial forms of adjectives" that modify another adjective. 酷くてまずい means "terrible, and yucky".)
So I think the ku-form ...