Find an equation for the parabola described.
-Vertex at $( 3 , - 4 )$; focus at $( 3 , - 6 )$
A) $( x - 3 ) ^ { 2 } = 8 ( y + 4 )$
B) $( x - 3 ) ^ { 2 } = - 8 ( y + 4 )$
C) $( y - 4 ) ^ { 2 } = - 12 ( x + 3 )$
D) $( y - 4 ) ^ { 2 } = 12 ( x + 3 )$

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. Here, the vertex is $(3, -4)$ and the focus is $(3, -6)$, indicating the parabola opens downward (since the focus is below the vertex) and $p = 2$ (the distance from the vertex to the focus). Substituting $h = 3$, $k = -4$, and $p = -2$ (negative because the parabola opens downward) into the vertex form gives $(x - 3)^2 = -8(y + 4)$.

Find an Equation for the Parabola Described (3,−4)( 3 , - 4 )(3,−4)

Find an Equation for the Parabola Described $( 3 , - 4 )$