I suggest you take a look at this chapter in the user manual. It gives details about QPs in CPLEX.
For continuous QP CPLEX can use different algorithms (such as quadratic simplex, barrier, ...) and you can configure what you want CPLEX to use.
If integer variables are involved then CPLEX will do branch and bound as for regular MIP. The only difference is that the relaxations at the nodes are then solve as QPs rather than LPs.
#CPLEXOptimizers#DecisionOptimization