We study in detail the lower semicontinuity and the upper semicontinuity properties of the set-valued map $(D,A,c,b)\to \mathrm{sol}(D,A,c,b),$ where $\mathrm{sol}(D,A,c,b)$ denotes the solution set of the quadratic programming problem
$$\text{Minimize }f(x):=c^{T}x+{\displaystyle \frac{1}{2}}{x}^{T}Dx\text{ subject to }Ax\ge b,x\ge 0.$$
In particular, a complete characterization for the lower semicontinuity of the map $\mathrm{sol}(\cdot )$ is obtained.