The tricritical points of a quenched site-diluted spin-1 Ising model, containing both biquadratic exchange and single-ion anisotropy in addition to the usual bilinear exchange interactions, are studied by using an effective field theory. In doing so particular attention is paid to the approximation made in effecting the configurational averaging. The concentration dependence of the location of the tricritical points in the temperature versus single-ion anisotropy plane is studied for a range of interaction strengths, and the critical concentration below which the tricritical points are absent is determined for the simple cubic, square and honeycomb lattices.