ATV dealers must abide by the age recommendations when selling quads (this is set by the manufacturers not the state)
And as BigBear has stated the only restrictions, about riding,(cc wise from the state) are 8&9 y/o are limited to 70 cc or less.
With one note....the 8-16 sounds confusing... a 16 y/o does not need the certification.
The certification has nothing to do with state trails....if a child ages 8-15 wants to ride off of the property that is owned by their PARENTS, they must have a safety certification, this includes private trails as well as state trails, and even grandpa or uncle Joes farm.