We consider a quadratic programming method designed for use in a sequential quadratic programming (SQP) method for large-scale nonlinearly constrained optimization. Because the efficiency of SQP methods is determined by how the quadratic subproblem is formulated and solved, we propose an active-set method based on inertia control that prevents singularity in the associated KKT systems. The method is able to utilize black-box linear algebra software, thereby exploiting recent advances in computer hardware. Moreover, the method makes no assumptions on the convexity of the quadratic problems making it particularly useful in SQP methods using exact second derivatives. In addition, the method can be applied to a regularized quadratic subproblem involving an augmented Lagrangian objective function, eliminating the need for a full-rank assumption on the constraint matrix.