Find the vertex and focus of the parabola. $( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0$
A)vertex: $( 3,7 )$ focus: $( 3,7 )$
B)vertex: $( 3,7 )$ focus: $( - 9 , - 3 )$
C)vertex: $( 3,7 )$ focus: $( 3,23 )$
D)vertex: $( - 3 , - 7 )$ focus: $( - 3 , + 7 )$
E)vertex: $( - 3 , - 7 )$ focus: $( 1 , - 7 )$

Question

Quizplus · Accepted Answer

The given equation is in the form $(y-k)^2 = 4p(x-h)$, where the vertex is at $(h, k)$ and the focus is at $(h+p, k)$. Rearranging the given equation to match this form, we find the vertex is $(-3, -7)$. With $4p = 16$, we get $p = 4$, so the focus is $(1, -7)$.

Find the Vertex and Focus of the Parabola (y+7)2−16(x+3)=0( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0(y+7)2−16(x+3)=0

Find the Vertex and Focus of the Parabola $( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0$