My ex-girlfriend moved my daughter out of state last year. I have paid support for 9 yrs. I do not get to see my daughter because of the move and I cannot afford to go back to court. How do I go about relinquishing my rights and does my ex need to approve?

You can not afford to go back to court but you can afford to relinquish your rights? Had you seen your daughter until the move? Think long and hard, IF you can even relinquish your rights (which you probably can't) you will only remove your right to have any say in her upbringing and any right to see her, you will not remove your obligation to pay child support. Voluntary removal of your rights depends on a lot of different factors and will ultimately be up to the Court to decide if it will be granted in the best interest of your daughter. It will cost you to do this also. You won't be able to do it for free.

Quit your job, stop what you are doing and show your daughter that you actually care about her. Go where she goes, take control! Good idea?

First relinquishing or giving up your rights, has nothing to do with paying child support. ( unless a step parent wants to adopt)
You just lose any rights to visit, but still have to pay.
If you are paying too much, you can have the amount reviewed by the court if your income has changed and you are paying too much.

But why did you allow the move without terms for your visit, that is what you had the right to contest in court before she moved.

But sorry give up rights or not, child support will continue.