Write an equation for the parabola.
-vertex $( - 6 , - 7 )$, focus $( - 6 , - 11 )$
A) $( x - 6 ) ^ { 2 } = - 44 ( y - 7 )$
B) $( x + 6 ) ^ { 2 } = - 16 ( y + 7 )$
C) $16 ( y - 7 ) = ( x - 6 ) ^ { 2 }$
D) $16 ( y - 6 ) = ( x - 7 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The vertex form of a parabola that opens up or down is $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex and $p$ is the distance from the vertex to the focus. Given the vertex $(-6, -7)$ and the focus $(-6, -11)$, the distance $p = -4$ (since the focus is 4 units below the vertex, indicating the parabola opens downwards). Substituting $h = -6$, $k = -7$, and $p = -4$ into the vertex form equation gives $(x + 6)^2 = -16(y + 7)$, which matches choice B.

Write an Equation for the Parabola (−6,−7)( - 6 , - 7 )(−6,−7)

Write an Equation for the Parabola $( - 6 , - 7 )$