Write an equation for the parabola.
-vertex $( - 3 , - 9 )$, focus $( - 3 , - 11 )$
A) $( x - 3 ) ^ { 2 } = - 44 ( y - 9 )$
B) $8 ( y - 9 ) = ( x - 3 ) ^ { 2 }$
C) $( x + 3 ) ^ { 2 } = - 8 ( y + 9 )$
D) $8 ( y - 3 ) = ( x - 9 ) ^ { 2 }$

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 $(-3, -9)$ and the focus $(-3, -11)$, the parabola opens downward (since the focus is below the vertex), and $p = -2$ (the distance from the vertex to the focus). Substituting $h = -3$, $k = -9$, and $p = -2$ into the vertex form gives $(x + 3)^2 = -8(y + 9)$, which matches choice C.

Write an Equation for the Parabola (−3,−9)( - 3 , - 9 )(−3,−9)

Write an Equation for the Parabola $( - 3 , - 9 )$