Graph Parabolas with Vertices Not at the Origin
Find the vertex, focus, and directrix of the parabola with the given equation.
-$( y - 4 ) ^ { 2 } = - 16 ( x - 2 )$
A) vertex: $( 2,4 )$
focus: $( - 2,4 )$
directrix: $x = 6$
B) vertex: $( - 2 , - 4 )$
focus: $( - 6 , - 4 )$
directrix: $x = 2$
C) vertex: $( 4,2 )$
focus: $( 0,2 )$
directrix: $x = 8$
D) vertex: $( 2,4 )$
focus: $( 6,4 )$
directrix: $x = - 2$

Question

Quizplus · Accepted Answer

We can rearrange the given equation into the standard form of a parabola 
$$(x-h)^2=4p(y-k)$$ by completing the square. We obtain 
$$(y-4)^2=-16(x-2)\Rightarrow (y-4)^2=-16(x-2-1)$$ 
Now, we can identify the vertex as $(h,k)=(2,4)$ and $4p=-16\Rightarrow p=-4$. 
Therefore, the focus is located at $(h,k+p)=(2,0)$ and the directrix is the horizontal line $y=k-p=4+4=8$. 
Thus, the correct choice is (A).

Graph Parabolas with Vertices Not at the Origin Find the Vertex

Graph Parabolas with Vertices Not at the Origin
Find the Vertex