Find the vertex and focus of the parabola. $( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0$
A)vertex: $( 6 , - 3 )$ focus: $( 6,5 )$
B)vertex: $( 6 , - 3 )$ focus: $( 6 , - 11 )$
C)vertex: $( 6 , - 3 )$ focus: $( 4 , - 3 )$
D)vertex: $( - 6,3 )$ focus: $( - 8,3 )$
E)vertex: $( - 6,3 )$ focus: $( - 6 , - 3 )$

Question

Quizplus · Accepted Answer

The given equation is $(y - 3)^2 + 8(x + 6) = 0$. Rearranging, we get $(y - 3)^2 = -8(x + 6)$. This is a parabola that opens to the left since the squared term is $y$ and the coefficient of $x$ is negative. The vertex form of a parabola that opens left or right is $(y - k)^2 = 4p(x - h)$, where $(h, k)$ is the vertex and $p$ is the distance from the vertex to the focus. Comparing, we find the vertex is $(-6, 3)$. With $4p = -8$, we get $p = -2$, indicating the focus is 2 units to the left of the vertex, making the focus $(-8, 3)$.

Find the Vertex and Focus of the Parabola (y−3)2+8(x+6)=0( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0(y−3)2+8(x+6)=0

Find the Vertex and Focus of the Parabola $( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0$