would 뒤에 동사원형인가요?

would 도 조동사 이니깐 would 뒤에 오는 동사는 동사 원형을 취하는거 맞나요?

예를 들어서

the teacher was reparied, so margie would have to go to school today.

와

why would anyone write about school?그리고두 문장에서 would 가 갖는 의미? 라 해야하나 .. 기능 같은건 뭔가요 ㅠㅠ