This paper formulates a simplied trajectory smoothing model for guiding movements of connected automated vehicles on a general one-lane highway segment. This simplied problem constructs each vehicle trajectory as a piece-wise quadratic function with no more than ve pieces and lets all trajectories share identical acceleration and deceleration rates. This paper investigates theoretical properties of this problem structure and proposes an exact analytical algorithm that very eciently solves the optimal solution. Numerical example are conducted to illustrate how to apply this model to CAV control problems on signalized segments and at non-stop intersections.