Aerodynamic noise is an important criterion in the design of aircraft and wind turbines. Addressing noise at the aircraft conceptual design phase is required to properly account for the multidisciplinary nature of the problem. A fundamental understanding of how the airfoil and wing shapes affect the trailing-edge (TE) noise is therefore necessary. In this paper, we investigate the relationship between the airfoil TE noise and its basic shape parameters, such as camber and thickness ratio. A recently developed noise metric model, which is based on computational fluid dynamic simulations using the steady Reynolds-Averaged Navier-Stokes equations, is used. Parametric and optimization studies reveal that the maximum camber, the location of maximum camber, and the thickness ratio have significant effect on the noise metric. The results of optimization show that an airfoil with maximized aerodynamic performance does not have minimum noise metric value, indicating that a trade-off is necessary when considering noise as a part of airfoil design.