Final answer:
The vertex of the quadratic function f(x)=-2(x+1)²+4 is located at (-1, 4), which can be determined by understanding that the function is in vertex form.
Step-by-step explanation:
To determine the coordinates of the vertex for the quadratic function f(x)=-2(x+1)²+4, we can use the fact that this function is in vertex form, which is f(x)=a(x-h)²+k, where (h, k) is the vertex of the parabola. In this case, the values of h and k can be read directly from the function: h = -1 and k = 4, because the formula has (x+1) corresponding to (x-h), indicating that h = -1. Therefore, the vertex of the parabola for the function f(x) is (-1, 4).