Find the standard form of the equation of the parabola.
-Vertex at $( - 7 , - 2 )$, opens to the left, focal width $= 14$
A) $( y + 2 ) ^ { 2 } = - 14 ( x + 7 )$
B) $( y + 2 ) ^ { 2 } = 14 ( x + 7 )$
C) $( y + 2 ) ^ { 2 } = - 3.5 ( x + 7 )$
D) $( x + 7 ) ^ { 2 } = 14 ( y + 2 )$

Question

Quizplus · Accepted Answer

The standard form of a parabola opening to the left or right is $(y-k)^2=4p(x-h)$, where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the focus. Given the focal width is $14$, $4p=14$, so $p=-3.5$ (negative because the parabola opens to the left). Thus, the equation is $(y+2)^2=-14(x+7)$.

Find the Standard Form of the Equation of the Parabola (−7,−2)( - 7 , - 2 )(−7,−2)

Find the Standard Form of the Equation of the Parabola $( - 7 , - 2 )$