The exact analytic and steady-state solutions are derived for high-order Gaussian beam propagation modes in media with quadratic radial refractive index and gain (loss) profiles based on the slowly varying envelope approximation (SVEA). Explicit expressions of the solutions are given for some useful specific cases. Possible applications of the present theory to optical cavities and waveguides with such media and to problems of optical bistability in cavities having media with quadratic radial index and absorption profile are discussed.