Find the axis of symmetry and what direction the parabola opens.
-1/4(y+4)=(x-3)²

First, convert the equation to the standard equation of a parabola.
-1/4(y+4)=(x-3)^2     ---multiply -4 on both sides   
y+4=-4(x-3)^2           ---subtract 4 on both sides
y=-4(x-3)^2-4
From the equation, we know that the parabola was moved by 3 to the right, because of (x-3)^2. So the axis of symmetry is x=3. Now look at the number in front of (x-3)^2. It is -4. Since it is negative, the parabola opens downwards. 

Equation of parabola ==> (y-k) = a(x-h)²

To find te direction of this parabola, multiply both sides by (-1) ==>
1/4(y+4) - (x+3)². Since "a" is negative, the parabola opens downward & hence it's Vertex is a MAXIMUM.

Let's calculate this Maximum:
Vertex (h , k) and Axis of symmetry x=h

The given function: -1/4(y+4)=(x-3)², where k=- 4 & h= +3

Hence the axis of symmetry is x=3 & the vertex is at (3, -4)