Is it possible, in Massachusetts, for both parents to give up parental rights to their kid (17y/o) and have the kid adopted by another family?

And if so, can this be done without having to go to court, like by just signing some papers or whatever and that be it..

At 17 - depending on the reason this is being done - it is easier to emancipate "the kid" - OR declare him/her to be a person in need of supervision (or a similar term) and request placement in the foster care or some other similar system.

Yes, both parents can consent to an adoption but it must go through a Court process.

Parents can also name a Guardian for the child and, depending on the circumstances, pretty much walk away.

Until the child is adopted, emancipated or of legal age the parents MUST support the child.

This is a legal question.

Does the child want to be adopted, and the purpose is also an issue, but no, it can not be done by signing a few papers, you will have to go though court, have investigations, and more by the courts. The child would be 18 before it was finsihed at this point