Abstract: This talk presnets the quadratic programming over a quadratic constraint by the canonical dual approach, where the objective and the constraint matrices may be both indefinite. Under the dual Slater's condition, we show that the canonical dual functional is smooth concave and has a finite supremum unless the primal quadratic problem is infeasible. Moreover, the supremum always equals to the minimum value of the primal and we can apply a dual-to-primal conversion plus a so-called ``boundarification'' technique to bring the dual solution to a global minimizer of the primal. The results can be used to solve a (nonconvex) quadratic problem over a ball with error bound estimations.