Learn French: Est-ce que tu veux goûter quelque chose ?

You actually can just ask Tu veux goûter quelque chose ? in casual spoken French! However, placing est-ce que at the beginning of a statement is the standard way to turn it into a yes/no question. It lets you ask a question without having to change the word order of the sentence.

Why does goûter end in '-er' instead of being conjugated to match tu?

In French, when you have two verbs right next to each other, only the first one is conjugated. Since veux (the 'you' form of 'to want') is already conjugated, the second verb goûter (to taste) stays in its dictionary form, which is called the infinitive.

How does quelque chose fit into a lesson about negative adverbs?

Quelque chose means 'something,' which is a positive statement. In lessons about negative adverbs, you will often learn how to say the opposite. The negative opposite of quelque chose is ne... rien (nothing/not anything). If you wanted to say 'You do not want to taste anything,' you would say Tu ne veux rien goûter.

Is goûter related to the French word for a snack?

Yes! Here it is used as a verb meaning 'to taste.' But in France, le goûter is also the name of a very popular sweet afternoon snack that children eat after school.