Except in desperate situations, a team will generally attempt a field goal only when keeping a drive alive is unlikely, and their kicker has a significant chance of success, as a missed field goal results in a turnover at the spot of the kick in the NFL; in the NCAA it's at the spot of the snap.
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In the NFL, where the ball is kicked from. So if the ball is spotted on the 20 the kicker will usually line up 7 yards back, if he misses the other team gets the ball at the 27. If the kick was attempted from inside the 20, the ball is placed at the 20.
In college football, the ball is spotted at the original line of scrimmage.
In high school, the ball is placed at the 40-yard line. In the NFL, it is placed at the 35.
30 yards from where the ball was kicked off. If the kickoff was at the kicking team's 30 yard line, the ball will be placed at the offensive team's 40 yard line.