Here is the item:
Rachel would have wrote a better essay for
Professor Parker, but she drank
a double espresso and found
that she had too much energy to sit still at the computer.
The first verb, would have wrote, is incorrect. As you recognized, this verb requires the past participle written because of the auxiliary verbs would and have.
Write is an irregular verb; the chart below shows its forms.
| Verb | Simple Present |
Simple Past |
Past Participle |
|---|---|---|---|
| write | write(s) | wrote | written |