Graph Parabolas with Vertices Not at the Origin
Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( y + 2 ) ^ { 2 } = 20 ( x + 3 )$$
A) vertex: $( - 3 , - 2 )$
focus: $( 2 , - 2 )$
directrix: $x = - 8$
B) vertex: $( 3,2 )$
focus: $( 8,2 )$
directrix: $x = - 2$
C) vertex: $( - 2 , - 3 )$
focus: $( 3 , - 3 )$
directrix: $x = - 7$
D) vertex: $( - 3 , - 2 )$
focus: $( - 8 , - 2 )$
directrix: $x = 2$

Question

Quizplus · Accepted Answer

The given equation is in the form $(y-k)^2=4p(x-h)$, where $(h,k)$ is the vertex. Thus, the vertex is $(-3,-2)$. The value of $4p$ is 20, so $p=5$, indicating the focus is 5 units to the right of the vertex, making the focus $(2,-2)$, and the directrix is $x=-8$, 5 units to the left of the vertex.

Graph Parabolas with Vertices Not at the Origin Find the Vertex

Graph Parabolas with Vertices Not at the Origin
Find the Vertex