Write an equation for the parabola.
-vertex: $( 3 , - 4 )$, directrix: $x = 11$
A) $( x + 4 ) ^ { 2 } = - 32 ( y - 3 )$
B) $x ^ { 2 } = - 32 ( y - 3 )$
C) $( y + 4 ) ^ { 2 } = - 32 ( x - 3 )$
D) $( y - 3 ) ^ { 2 } = - 32 ( x + 4 )$

Question

Quizplus · Accepted Answer

The vertex form of a parabola that opens horizontally is $(y - k)^2 = 4p(x - h)$, where $(h, k)$ is the vertex and $p$ is the distance from the vertex to the directrix. Given the vertex $(3, -4)$ and the directrix $x = 11$, the parabola opens to the left (since the directrix is to the right of the vertex), and $p = 8$ (the distance from the vertex to the directrix). Substituting $h = 3$, $k = -4$, and $p = -8$ (negative because the parabola opens to the left) gives $(y + 4)^2 = -32(x - 3)$.

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

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