Which sentence is grammatically correct?

The sentence "Sarah plays her new saxophone well" is grammatically correct because it uses "well" as an adverb to describe how Sarah plays the saxophone. In English, adverbs modify verbs and typically answer the question of how, when, where, or to what extent. In this context, "well" effectively communicates that Sarah's performance is of a high quality.

In contrast, the other sentences misuse the word "good," which is an adjective, instead of using the appropriate adverb "well." For instance, "The dog catches the frisbee good" should use "well" to accurately describe how the dog performs the action of catching. Similarly, "The band did good during the half time show" is incorrect because "did" requires an adverb, and "the band that played before ours was well" also misuses "well," as it does not describe an action or state in this context.