This is the 14301st most frequent Russian word.
отвечавший
"One who answered" or "answered" (past participle).
Here, 'отвечавший' is used as a past participle that modifies 'учитель,' describing someone who performed the action of 'answering' in the past.
Учитель отвечавший на вопросы студентов выглядел уверенно.
The teacher who was answering the students' questions looked confident.
In this sentence, 'отвечавшую' is a modified form of 'отвечавший' agreeing in gender and case with the noun 'работу,' meaning the work met certain conditions.
Жюри отметило работу отвечавшую критериям конкурса.
The jury noted the work that met the contest criteria.
Here, 'отвечавшего' modifies 'человека' and also denotes someone who had responsibility (was 'answering for') in a specific context.