Well, the apple often does not fall far from the tree. Is it an accident, do you think, that the child is unmotivated and the parent(s) support this lack of commitment? Perhaps it may be that the parents just want to take the course of least resistance—again, this is something that we find with the students.
There are no guarantees that supportive parents will have motivated children, but it's closer to the norm than students who are motivated with uncaring parents. I can say that I've seen hard-working students whose parents are not in the picture (dead, in jail, etc.) Sometimes seeing the parent's (parents') mistakes will motivate kids who refuse to end up in the same place.
Of course, irony is king in education...because intelligent thought is so often overlooked. Demanding teachers are seen as "mean" by the kids, and as unrealistic or unreasonable by parents. I find that you need to have a tough skin, keep extremely accurate records, provide students with feedback on papers, and keep communication open with parents, even if only with quick notes or emails. It demonstrates your commitment to the student's success and defends your actions in the classroom.
More and more, apathy and laziness is a family attribute where learning is concerned. Isn't it amazing that in other countries education is such a priority and our kids and many parents think it doesn't matter? Is it any wonder that U.S. testing scores are dropping so radically? Very sad.