Verified answer

y^2 - 4y + 12 = -x

y^2 - 4y + 4 + 8 = -x

(y - 2)^2 + 8 = -x

x = -8 - (y - 2)^2

The vertex is at (2 , -8) and it opens to the left. This means that x must be greater than 2, so that narrows it down a bit

x + 8 = -(y - 2)^2

4p * (x + 8) = -(y - 2)^2

4p = 1

p = 1/4

2 + 1/4 = 9/4

x = 9/4 is the directrix, so I can't see how they got 5 either.

So the directrix is at 2 - (-1/4) = 2 + 1/4 = 9/4

x= -y^2 + 4y - 12

x=-(y^2-4y+4)-8

x=-(y-2)^2-8

-(x+8)=(y-2)^2

Directix is x= 1/4-8=-31/4

Answer must be x=-31/4

x does not equal 5, since we don't know the value of "Y" because both "Y"s are on the same side of the equal sign, and if you do get a "Y" on the other side, there's and "X" so you can't solve it!

x = -1y2 + 4y + -12

x = -12 + 4y + -1y2

x = -12 + 4y + -1y2

x = -12 + 4y + -1y2