Final answer:
The vertex of the parabola described by the equation g(x)=-2(x-2)² +3 is the ordered pair (2, 3).
Step-by-step explanation:
The function g(x)=−2(x−2) ^2+3 is written in vertex form g(x)=a(x−h) ^2 +k, where (h,k) represents the vertex of the parabola. In this equation, the vertex is at (h,k)=(2,3). The form g(x)=a(x−h) ^2+k allows for immediate identification of the vertex: (h,k) represents the horizontal and vertical shifts respectively from the standard parabolic form. Here, h=2 corresponds to the horizontal shift, and k=3 corresponds to the vertical shift. Thus, the vertex of the function g(x)=−2(x−2) ^2+3 is the ordered pair (2,3), indicating that the parabola opens downwards and reaches its maximum point at x=2 with a corresponding y-value of 3.