Question

What is the directrix of the parabola defined by 1/4(y+3)=(x-2)^2

Answer 1

This is a parabola which opens upwards and the directrix will be of the form  
y = k

the general form is 

4p(y - k) = (x - h)^2   we have:-

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

so the vertex is at (2, -3)

4p = 1/4  so p =  1/16

so the focus will be at (2 , -2 15/16)

and directrix is  y = -3 1/16