We derive analytical solutions that describe the one-dimensional displaced and chirped symmetric Pearcey Gaussian beam in a uniformly moving parabolic potential. The multiple effective manipulations of the beam, which are originated from the diverse configurations of the dynamic parabolic potential, are demonstrated. On the whole, the accelerating trajectory can transform into a linear superposition form of the oblique straight line and the simple harmonic motion. Meanwhile, we discuss the further modulation of the accelerating trajectory characteristics such as slope, amplitude and phase shift. Additionally, the extension into a two-dimensional scenario is also proposed. Our results theoretically improve the practical value of the Pearcey beam, and lead to potential applications in trajectory manipulation and particle manipulation.