The energy levels and lattice vibrational modes in quantum dots (QDs) become discrete due to 3D quantum confinement. Therefore, the influence of electron-phonon (e-p) interaction on physical properties of QDs is an important subject to study. In this work, the effects of e-p interaction and pressure in a GaAs wedge-shaped (WS) quantum dot are considered. In first step, using the dielectric continuum model, the Hamiltonian of longitudinal optical (LO) phonons and the e-p interaction Hamiltonian are analytically derived. In the next step, we have studied the e-p effect on energy eigenvalues, magnetic susceptibility and optical properties of the WS quantum dot. We have also investigated the pressure effect on optical properties of the system in the presence of the e-p interaction. It is found that the polaronic energy shift reduces when the QD size increases. The magnetic susceptibility enhances with raising the QD size. The e-p effect on magnetic susceptibility is strong for smaller QD sizes. The absorption coefficient shows two peaks in the presence of the e-p interaction. The refractive index change enhances and moves to higher energies under the e-p interaction. We found that the pressure and e-p interaction, simultaneously, have important effects on absorption coefficient and refractive index changes.