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

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 $(4, -2)$ and the directrix $x = 9$, the distance $p = 4 - 9 = -5$. Substituting $h = 4$, $k = -2$, and $p = -5$ into the vertex form gives $(y + 2)^2 = -20(x - 4)$.

Write an Equation for the Parabola (4,−2)( 4 , - 2 )(4,−2)

Write an Equation for the Parabola $( 4 , - 2 )$