Is this answer correct on problem 3

-1/4*x^2-x+3=-1/4*(x^2+4x)+3=-1/4*(x^2+4x+4)+4=-1/4*(x+2)^2+4
x0=-2

This is a vertical parabola which opens downwards

Use the formula

4p(y - k) =  (x - h^2

converting to  vertex form-
y =
-1/4(x^2 + 4x) + 3
y = -1/4[ (x + 2)^2] + 4

y - 4  =  -1/4 (x + 2)^2

-4(y - 4) =  (x + 2)^2  so the vertex is at (-2, 4)
comparing with the above formula
4p = -4
so p = -1  where p is the distance of the focus from the vertex
The vertex is at  (-2,4)  so the focus is at  (-2, 4-1)  = (-2, 3) Answer

(1/x + 1)^2 + 6 (1/x + 1) +5