Graph Parabolas with Vertices Not at the Origin
-$( \mathrm { y } + 1 ) ^ { 2 } = - 12 ( \mathrm { x } + 2 )$
A) vertex: $( - 2 , - 1 )$
focus: $( - 5 , - 1 )$
directrix: $x = 1$
B) vertex: $( 2,1 )$
focus: $( - 1,1 )$
directrix: $x = 5$
C) vertex: $( - 1 , - 2 )$
focus: $( - 4 , - 2 )$
directrix: $x = 2$
D) vertex: $( - 2 , - 1 )$
focus: $( 1 , - 1 )$
directrix: $x = - 5$

Question

Quizplus · Accepted Answer

The given equation $(y + 1)^2 = -12(x + 2)$ is in the form $(y - k)^2 = 4p(x - h)$, where the vertex is at $(h, k)$ and $p$ is the distance from the vertex to the focus and to the directrix. Here, $h = -2$, $k = -1$, and $4p = -12$, so $p = -3$. The vertex is $(-2, -1)$, the focus is $(-2 - 3, -1) = (-5, -1)$, and the directrix is $x = -2 + 3 = 1$.

Graph Parabolas with Vertices Not at the Origin - (y+1)2=−12(x+2)( \mathrm { y } + 1 ) ^ { 2 } = - 12 ( \mathrm { x } + 2 )(y+1)2=−12(x+2)

Graph Parabolas with Vertices Not at the Origin
- $( \mathrm { y } + 1 ) ^ { 2 } = - 12 ( \mathrm { x } + 2 )$