Write an equation for the parabola.
-vertex: $( - 4,1 )$, directrix: $x = - 9$
A) $( x - 1 ) ^ { 2 } = 20 ( y + 4 )$
B) $( y - 1 ) ^ { 2 } = - 20 ( x + 4 )$
C) $( y - 1 ) ^ { 2 } = 20 ( x + 4 )$
D) $( x + 4 ) ^ { 2 } = - 20 ( x - 1 )$

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 $(-4, 1)$ and the directrix $x = -9$, the distance $p = 5$ (since the vertex is 5 units to the right of the directrix). Thus, the equation is $(y - 1)^2 = 20(x + 4)$, matching choice C.

Write an Equation for the Parabola (−4,1)( - 4,1 )(−4,1) , Directrix

Write an Equation for the Parabola $( - 4,1 )$ , Directrix