Write Equations of Parabolas in Standard Form
Find the standard form of the equation of the parabola using the information given.
-Vertex: $( 3 , - 7 )$; Focus: $( 3 , - 6 )$
A) $( x - 3 ) ^ { 2 } = 4 ( y + 7 )$
B) $( x - 3 ) ^ { 2 } = - 4 ( y + 7 )$
C) $( y - 7 ) ^ { 2 } = 12 ( x + 3 )$
D) $( y - 7 ) ^ { 2 } = - 12 ( x + 3 )$

Question

Quizplus · Accepted Answer

The standard form of a parabola with a vertical axis (opening up or down) is $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex and $p$ is the distance from the vertex to the focus. Given the vertex $(3, -7)$ and the focus $(3, -6)$, the parabola opens upwards (since the focus is above the vertex), and $p = 1$. Substituting $h = 3$, $k = -7$, and $p = 1$ into the formula gives $(x - 3)^2 = 4(y + 7)$.

Write Equations of Parabolas in Standard Form Find the Standard (3,−7)( 3 , - 7 )(3,−7)

Write Equations of Parabolas in Standard Form
Find the Standard $( 3 , - 7 )$