What do I call a quote in an essay

After submitting my essay, my English teacher marked the word "quote" as an error. Is this incorrect word usage, and should I be using "excerpt," quotation," or "event" here? The quote is from Frederick Douglass's speech, "What to a Slave is the Fourth of July?"

“See, too, that girl of thirteen, weeping, yes! weeping, as she thinks of the mother from whom she has been torn.”

Although this quote was not from one of Douglass’s personal experiences, Douglass told it like a story, as though he was there.

Solution 1:

Quote and Quotation are perfect synonyms in their main meanings and both are extant.

OED

Quotation (n.) 5.a. A passage quoted from a book, speech, or other source; (in modern use esp.) a frequently quoted passage of this nature.

first recorded in 1621 and still current.

1962 S. Raven Close of Play i. iii. 38 ‘Sui memores..alios fecere merendo... It is a quotation’, said Hugo, ‘familiar to all men of even moderate education.’

2005 Oxford American. Fall 72/1 I planned to sprinkle the magic book liberally with quotations from Faulkner.

7. An amount stated as the price of a stock or of any commodity for sale. Also: a contractor's stated price for a particular job.

1944 R. V. Boughton in R. Greenhalgh Pract. Builder xii. 378/2 There are usually conditions which make it very prudent to obtain many quotations for each job as it is estimated.

1993 Gibbons Stamp Monthly Jan. 66/1 This stamp always has a hefty quotation in continental catalogues and despite its astronomical rise it is still worth acquiring if you can afford it.

Quote (n.) 2.a. A quoted passage or remark; = quotation n. 5.Recorded earliest in quote mark n. 1885.

1885 Pall Mall Gaz. 23 Jan. 6/1 The ‘interviewer’ (..has not the time come for leaving out the quote marks?).

1993 Humanist in Canada Winter 38/2 The categories with the largest numbers of Russel quotes include Belief, Democracy, Education.

3. = quotation n. 7.

1934 Brainerd (Minnesota) Daily Dispatch 31 Dec. 3/5 The following are today's custom smelters' quotes for delivered copper (cents per pound).

To me, "quotation" is slightly more formal and I agree with your teacher's advice on the basis of (i) style and (ii) no examiner will object to "quotation".