Graph Parabolas with Vertices Not at the Origin
-$$( y - 2 ) ^ { 2 } = 4 ( x - 3 )$$
A) vertex: $( 3,2 )$
focus: $( 4,2 )$
directrix: $x = 2$
B) vertex: $( - 3 , - 2 )$
focus: $( - 2 , - 2 )$
directrix: $x = - 4 \quad$
C) vertex: $( 2,3 )$
focus: $( 3,3 )$
directrix: $x = 1$
D) vertex: $( 3,2 )$
focus: $( 2,2 )$
directrix: $x = 4$

Question

Graph Parabolas with Vertices Not at the Origin
-$$( y - 2 ) ^ { 2 } = 4 ( x - 3 )$$
A) vertex: $( 3,2 )$
focus: $( 4,2 )$
directrix: $x = 2$
B) vertex: $( - 3 , - 2 )$
focus: $( - 2 , - 2 )$
directrix: $x = - 4 \quad$
C) vertex: $( 2,3 )$
focus: $( 3,3 )$
 directrix: $x = 1$
D) vertex: $( 3,2 )$
focus: $( 2,2 )$
directrix: $x = 4$

Quizplus · Accepted Answer

The given equation is in the form $(y-k)^2=4p(x-h)$, where $(h,k)$ is the vertex, indicating the vertex is at $(3,2)$. The value of $4p$ is 4, so $p=1$, meaning the focus is 1 unit right from the vertex at $(4,2)$, and the directrix is $x=h-p$, which is $x=2$.

Graph Parabolas with Vertices Not at the Origin - (y−2)2=4(x−3)( y - 2 ) ^ { 2 } = 4 ( x - 3 )(y−2)2=4(x−3)

Graph Parabolas with Vertices Not at the Origin
- $( y - 2 ) ^ { 2 } = 4 ( x - 3 )$