What are the types of vertical curves and their purposes?

Vertical curves connect grade changes on highways. Crest curves are convex (summit) and designed for sight distance - drivers must see over the curve. Sag curves are concave (valley) and designed for headlight sight distance at night and passenger comfort. Both use parabolic geometry for smooth transitions. Curve length depends on design speed and algebraic difference in grades. Drainage considerations important at sag curves to prevent water accumulation.