Find the coordinates of the vertex, the equation of the axis of symmetry, and the direction the parabola opens of (x+2)^2 -4y -4=0

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex and a is the slope of the parabola that tells how wide or narrow the vertex is and whether it opens up or down. With what you were given, we must first solve for y: 4y = (x + 2)^2 - 4 now divide by 4:
y = 1/4 (x + 2)^2 - 1 so the vertex is (-2,-1) and a is 1/4. Since a is positive, the parabola opens up.
The axis of symmetry is he vertical line that runs. Straight up and down through the middle of the parabola. Since the vertex is (-2, -1) and vertical lines have the formula x = (whatever the x value is) , the equation for the line of symmetry is x = -2