Write Equations of Parabolas in Standard Form
Find the standard form of the equation of the parabola using the information given.
-Vertex: $( 4 , - 6 )$; Focus: $( 8 , - 6 )$
A) $( y + 6 ) ^ { 2 } = 16 ( x - 4 )$
B) $( y + 6 ) ^ { 2 } = - 16 ( x - 4 )$
C) $( x + 4 ) ^ { 2 } = - 8 ( y - 6 )$
D) $( x + 4 ) ^ { 2 } = 8 ( y - 6 )$

Question

Quizplus · Accepted Answer

The standard form of a parabola with a horizontal axis is $(y-k)^2=4p(x-h)$, where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the focus. Here, the vertex is $(4,-6)$ and the focus is $(8,-6)$, indicating a horizontal parabola with $p=4$. Substituting $h=4$, $k=-6$, and $p=4$ into the formula gives $(y+6)^2=16(x-4)$.

Write Equations of Parabolas in Standard Form Find the Standard (4,−6)( 4 , - 6 )(4,−6)

Write Equations of Parabolas in Standard Form
Find the Standard $( 4 , - 6 )$