Write an equation for the parabola.
-vertex: $( - 3 , - 4 )$, directrix: $x = - 8$
A) $( x + 4 ) ^ { 2 } = 20 ( y + 3 )$
B) $( y + 4 ) ^ { 2 } = 20 ( x + 3 )$
C) $( y + 4 ) ^ { 2 } = - 20 ( x + 3 )$
D) $( x + 3 ) ^ { 2 } = - 20 ( x + 4 )$

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 $x = -8$, the distance $p = 5$ (since the vertex is 5 units to the right of the directrix). The parabola opens to the right (positive direction) because the directrix is to the left of the vertex. Substituting $h = -3$, $k = -4$, and $4p = 20$ into the equation gives $(y + 4)^2 = 20(x + 3)$.

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

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