Take another look at the sentence:
Rachel would have wrote a better essay for Mr. Parker, but she drank a double espresso and found that she had too much energy to sit still at a computer.
Write is an irregular verb; the chart below shows its forms.
|Verb||Simple Present||Simple Past||Past Participle|
Drank, the verb you chose, is perfectly correct. Before you continue, review the rules for irregular verbs.