Learn German: Wir haben die Antwort gesucht.

In the German conversational past tense (Perfekt), you use two verbs. The helping verb (here, haben) takes the normal second position in the sentence, while the past action word (gesucht) gets pushed all the way to the end.

Wait, doesn't this lesson focus on verbs with a vowel change? Why is it gesucht?

Good catch! The verb suchen (to search) is actually a completely regular verb. It gets the ge- prefix and a -t at the end (ge-such-t), but its vowel stays exactly the same. Contrast this with the mixed verbs in this lesson (like bringen becoming gebracht), which take that same -t ending but do change their vowel.

Why do we use haben to make the past tense here instead of sein?

Most verbs in German use haben (to have) as their helping verb. You generally only use sein (to be) for verbs that express a change of location (like going or running) or a change of state (like waking up or dying). Since searching doesn't involve traveling from point A to point B, it takes haben.

The English translation says "looked for", but where is the word for "for" in the German sentence?

The German verb suchen means "to look for" or "to search" all on its own. You don't need to add a preposition like für. You just directly state the thing you are searching for right after it.