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 in the form $(y-k)^2 = 4p(x-h)$, where $(h, k)$ is the vertex. Rewriting the equation as $(y-3)^2 = -8(x+6)$, we identify $h = -6$, $k = 3$, and $4p = -8$, so $p = -2$. The vertex is $(-6, 3)$, and the focus, located $p$ units from the vertex in the direction of the parabola's opening, is $(-6-2, 3) = (-8, 3)$.

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 $( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0$