How would you draw the syntax tree of the sentence below?
She arrived at quarter past two
My doubts are especially about at quarter past two.
"at quarter past two" is a prepositional phrase, where "two" is the object, "past" is an adjective describing the two, and quarter is an adverb modifying past.
The entire prepositional phrase modifies "arrived". As an intransitive verb, it cannot take an object, but it can be modified.
This article on transitive and intransitive verbs explains it further.
It says:
The train from Montreal arrived four hours late.
The intransitive verb "arrived" takes no direct object, and the noun phrase "four hours late" acts as an adverb describing when the train arrived.
In this instance, the difference is "at" which turns it into a prepositional phrase acting adverbially.