In this paper, the trial function method is used to address the Lakshmanan-Porsezian-Daniel (LPD) equation with parabolic law nonlinearity. Implementing the traveling wave hypothesis reduces the LPD equation to an ordinary differential equation (ODE). From this ODE, many exact solutions, such as kink solitary wave solutions, bell shaped solitary wave solutions, triangular function solutions, periodic function solutions, singular solutions and Jacobian elliptic function solutions, are retrieved. Among them, some solutions are new. By suitable choice of parameters, we also draw 3D surface and 2D graphs of density, contour and level curves of some precise solutions for intuitive investigation.