Write an equation for the parabola.
-vertex: $( - 3,4 )$, directrix: $y = 10$
A) $( x + 3 ) ^ { 2 } = - 24 ( y - 4 )$
B) $( x + 3 ) ^ { 2 } = - 24 ( y + 4 )$
C) $( y + 3 ) ^ { 2 } = 8 ( x - 4 )$
D) $( y + 3 ) ^ { 2 } = - 24 ( x - 4 )$

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 or directrix. Here, the vertex is $(-3, 4)$ and the directrix is $y = 10$, which means the parabola opens downwards (since the directrix is above the vertex) and $p = 6$ (distance from vertex $y = 4$ to directrix $y = 10$). Substituting $h = -3$, $k = 4$, and $4p = -24$ (negative because the parabola opens downwards) gives $(x + 3)^2 = -24(y - 4)$.

Write an Equation for the Parabola (−3,4)( - 3,4 )(−3,4) , Directrix

Write an Equation for the Parabola $( - 3,4 )$ , Directrix