Write an equation for the parabola.
-vertex $( 5 , - 6 )$, focus $( 5,0 )$
A) $y - 6 = 24 ( x + 5 ) ^ { 2 }$
B) $24 ( y - 6 ) = ( x + 5 ) ^ { 2 }$
C) $( x - 5 ) ^ { 2 } = 24 ( y + 6 )$
D) $( y + 6 ) ^ { 2 } = 24 ( x - 5 )$

Question

Quizplus · Accepted Answer

The correct equation is derived using the formula for a parabola with a vertical axis of symmetry, $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex and $p$ is the distance from the vertex to the focus. Here, the vertex is $(5, -6)$ and the focus is $(5, 0)$, indicating a vertical axis and a $p$ of $6$. Thus, the equation is $(x - 5)^2 = 24(y + 6)$.

Write an Equation for the Parabola (5,−6)( 5 , - 6 )(5,−6)

Write an Equation for the Parabola $( 5 , - 6 )$