You just have your method take the parent class as the parameter...
public void animate(QuadBatch param) {
// animation code here
//if you need specific method calls you could cast the parameter here to a NewSprite
if (param instanceof NewSprite) {
NewSprite newSprite = (NewSprite)param;
//do NewSprite specific stuff here
}
}
//However, hopefully you have a method like doAnimate() on QuadBatch
//that you have overloaded in NewSprite
//and can just call it and get object specific results
public void animate(QuadBatch param) {
param.doAnimate();
}