Final answer:
The coordinates for the focus of the given parabola are (-3, 4).
Step-by-step explanation:
The equation (y-4)^(2)=-8(x+1) represents a parabola. To find the coordinates of the focus, we can rewrite the equation in a standard form for a parabola. Rearranging the equation, we get (y-4)^(2) = -8(x+1) which can be written as (y-4)^(2) = -8(x+1-0).
Comparing this with the standard equation (y-k)^(2) = 4a(x-h), we have (y-4)^(2) = -8(x+1-0) which means the vertex is at (h,k) = (-1,4) and the coefficient a = -2. The focus of the parabola can be found using the formula (h + a, k). Substituting the values, we get the coordinates of the focus as (-1 - 2, 4) = (-3, 4).