Graph Parabolas with Vertices Not at the Origin
-$$( y + 4 ) ^ { 2 } = 8 x$$
A) vertex: $( 0 , - 4 )$
focus: $( 2 , - 4 )$
directrix: $x = - 2$
B) vertex: $( 0,4 )$
focus: $( 3,4 )$
directrix: $x = - 1$
C) vertex: $( - 4,0 )$
focus: $( 2 , - 4 )$
directrix: $x = - 6$
D) vertex: $( 0 , - 4 )$
focus: $( - 3 , - 4 )$
directrix: $x = - 2$

Question

Quizplus · Accepted Answer

The equation $(y + 4)^2 = 8x$ is in the form $(y - k)^2 = 4p(x - h)$, where $(h, k)$ is the vertex. Here, $h = 0$ and $k = -4$, so the vertex is $(0, -4)$. The value of $4p = 8$, so $p = 2$, indicating the focus is 2 units to the right of the vertex at $(2, -4)$ and the directrix is a vertical line $x = -2$, 2 units to the left of the vertex.

Graph Parabolas with Vertices Not at the Origin - (y+4)2=8x( y + 4 ) ^ { 2 } = 8 x(y+4)2=8x

Graph Parabolas with Vertices Not at the Origin
- $( y + 4 ) ^ { 2 } = 8 x$