Learn Spanish (Latin America): Ella buscó sus raíces hace una semana.

In Spanish, to express "ago", you use the verb hacer in the form hace, followed by the amount of time. Literally, hace una semana means "it makes a week". Notice that in English we put "ago" after the time, but in Spanish, hace always comes before the time expression.

Why is there a "c" in raíces if the singular word is raíz?

In Spanish spelling, whenever a word ends in "z" and we make it plural by adding "es", the "z" changes to a "c" to keep the same sound. That is why raíz becomes raíces. It also keeps its accent mark so you remember to emphasize the "i".

Why isn't there a word for "for" after buscó?

The Spanish verb buscar already means "to look for" or "to search for" all by itself. You never need to add an extra word for "for" (like por or para) after it.

Why do we use the preterite tense buscó instead of the imperfect buscaba?

Because the sentence includes a specific, completed timeframe in the past (hace una semana), you must use the preterite tense. The imperfect tense (buscaba) would be used for ongoing or habitual past actions, like if you wanted to say "she used to look for her roots".