We are given the following function:
[tex]g(x)=-\frac{3}{2}(x-2)^2[/tex]We are asked to graph the function. To do that we notice that the function is a parabola of the form:
[tex]y=a(x-b)^2[/tex]It opens downwards since a < 0 and the x-intercept is 2 since b = 2. Therefore, the graph is: