Since the y coordinate of the focus is -4 and the directrix is y = -6 .....the focus lies above the directrix .....so....this parabola opens upward
The vertex lies 1/2 of the way between the focus and directrix......to find this we have ( -2, [ -4 + - 6] /2 ) =
(-2, -10/2 ) = (-2, -5) = (h, k)
"p' is the distance between the vertex and focus = l -5 - (-4) l = l -5 + 4 l = l -1 l = 1
So....we have the form
4p[ y - k ] = (x - h)^2
4(1) [ y - - 5 ] = (x - - 2)^2
4 ( y + 5) = ( x + 2)^2 multiply both sides by 1/4
y + 5 = (1/4)(x + 2)^2 subtract 5 from both sides
y = (1/4)(x + 2)^2 - 5