For child support purposes, the general rule is that a child is emancipated at age 18 or after he or she graduates high school, whichever is later. Thus, there is still the duty to support an 18 year old who is still in high school. A child can emancipate sooner than that, though, if he or she becomes self-supporting, which usually means getting married or joining the military, or something like that.
However, child support may continue past 18 and through age 21 if the child is in "a post-secondary educational institution", like college or a vocational school. In order for the child to remain eligible, though, the child or the custodial parent has a duty to report information from the school to the non-custodial parent. The requirements are pretty specific, so you should consult a lawyer or read section 452.340.5 of the Missouri Statutes very closely. Failure to provide this information may emancipate the child, but most cases on this point of law say that the child support obligation is merely abated for any semesters when the non-custodial parent doesn't receive this information as prescribed by 452.340.5. It is usually a question of whether the child is progressing towards a degree or trying to continue higher learning, as it is the public policy of the state to encourage children to seek higher education; thus courts frequently find that the support obligation should continue, so long as the child is trying to achieve this goal.