Graph Parabolas with Vertices Not at the Origin
Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( \mathrm { y } - 1 ) ^ { 2 } = 16 \mathrm { x }$$
A) vertex: $( 0,1 )$
focus: $( 4,1 )$
directrix: $x = - 4$
B) vertex: $( 0 , - 1 )$
focus: $( 6 , - 1 )$
directrix: $x = - 2$
C) vertex: $( 1,0 )$
focus: $( 4,1 )$
directrix: $x = - 3$
D) vertex: $( 0,1 )$
focus: $( - 6,1 )$
directrix: $x = - 4$

Question

Quizplus · Accepted Answer

The given equation is in the form $(y-k)^2=4p(x-h)$, where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the focus and directrix. Here, $h=0$, $k=1$, and $4p=16$, so $p=4$. Thus, the vertex is $(0,1)$, the focus, being $p$ units to the right of the vertex, is $(4,1)$, and the directrix, being $p$ units to the left of the vertex, is $x=-4$.

Graph Parabolas with Vertices Not at the Origin Find the Vertex

Graph Parabolas with Vertices Not at the Origin
Find the Vertex