Write Equations of Parabolas in Standard Form
-Vertex: $( 8 , - 6 )$; Focus: $( 8 , - 7 )$
A) $( x - 8 ) ^ { 2 } = - 4 ( y + 6 )$
B) $( x - 8 ) ^ { 2 } = 4 ( y + 6 )$
C) $( y - 6 ) ^ { 2 } = - 4 ( x + 8 )$
D) $( y - 6 ) ^ { 2 } = 4 ( x + 8 )$

Question

Quizplus · Accepted Answer

The vertex form of a parabola is $(x - h)^2 = 4p(y - k)$ for a parabola that opens up or down, where $(h, k)$ is the vertex. Since the focus is directly below the vertex, the parabola opens downward, making $p = -1$ (the distance from the vertex to the focus). Substituting $h = 8$, $k = -6$, and $p = -1$ into the formula gives $(x - 8)^2 = -4(y + 6)$.

Write Equations of Parabolas in Standard Form -Vertex (8,−6)( 8 , - 6 )(8,−6)

Write Equations of Parabolas in Standard Form
-Vertex $( 8 , - 6 )$