Does the bible say that when a child grows up they are to take care of their parents?
Behold, the third time I am ready to come to you; and I will not be burdensome to you: for I seek not yours, but you: for the children ought not to lay up for the parents, but the parents for the children. (2 Corinthians 12:14)
On the other hand, when Paul talks about widows that are supported by the church he says that children should support their parents who have no other support. Only a widow who had no relatives to support her could be supported by the congregation.
Honour widows that are widows indeed. But if any widow have children or nephews, let them learn first to show piety at home, and to requite their parents: for that is good and acceptable before God. Now she that is a widow indeed, and desolate, trusteth in God, and continueth in supplications and prayers night and day. But she that liveth in pleasure is dead while she liveth. And these things give in charge, that they may be blameless. But if any provide not for his own, and specially for those of his own house, he hath denied the faith, and is worse than an infidel. (1 Timothy 5:3-8)
If the parents are capable of self-support, then they should not rely on their children. Otherwise, the children should help their parents before relying on someone else to support them.