Many of us learned in school that adjectives modify nouns and that adverbs modify verbs. But as we’ve seen, adjectives can also act as complements for linking verbs. This leads to a common type of error: incorrectly substituting an adverb in place of a predicate adjective. An example you’ve probably heard before is:
Because “feel” is a verb, it seems to call for an adverb rather than an adjective. But “feel” isn’t just any verb; it’s a linking verb. An adverb would describe how you perform the action of feeling—an adjective describes what you feel. “I feel badly” means that you are bad at feeling things. If you’re trying to read Braille through thick leather gloves, then it might make sense for you to say “I feel badly.” But if you’re trying to say that you are experiencing negative emotions, “I feel bad” is the phrase you want.
It’s easier to see this distinction with a different linking verb. Consider the difference between these two sentences:
“Goober smells badly” means that Goober, the poor thing, has a weak sense of smell. “Goober smells bad” means Goober stinks—poor us.
from Grammarly Blog https://www.grammarly.com/blog/adjectives-and-adverbs/