Square root means that the expression x-3 cannot be negative, so x=3 is the low limit to the domain and is represented by (3,2) on the graph. Mark this point as critical. y=0 when the graph crosses the x-axis, that is: -0.5√(x-3)+2=0, √(x-3)=4, x-3=16, x=19, the point (19,0), which is another critical point on the graph to be marked. After crossing the x-axis the graph continues to descend.
The critical points help you to draw the graph, which is a semi-parabola (one of its arms).