Can you give me references on the responsibilities of parents?

They are to encourage their children:
1 Thessalonians 2:11 As ye know how we exhorted and comforted and charged every one of you, as a father doth his children,

They are to bring them up in the ways of the Lord and not wrongly provoke them:
Ephesians 6:4 And, ye fathers, provoke not your children to wrath: but bring them up in the nurture and admonition of the Lord.

And they should teach and train them:
Proverbs 22:6 Train up a child in the way he should go: and when he is old, he will not depart from it.

And they should correct them when necessary:
Proverbs 19:18 Chasten thy son while there is hope, and let not thy soul spare for his crying.

There are many other verses, but these are a good start. 🙂