in the function y = - 1/2 (x-1) ^2+3, what effect does the negative sign have on the graph, as compared to the graph of y=x^2?

The negative sign will have an effect in terms of which way the graph opens up. Since the function starts off negatively the graph will open down, like an upside down U. Rather if the function started off positive I. e Y=x^2 the graph will open upwards like a upright U.