Write an equation for the parabola with vertex at the origin.
-Through $( - 2,2 )$, opening to the left
A) $x = - 2 y ^ { 2 }$
B) $y ^ { 2 } = - 2 x$
C) $x = \frac { 1 } { 2 } y ^ { 2 }$
D) $x ^ { 2 } = 2 y$

Question

Quizplus · Accepted Answer

The correct equation for a parabola opening to the left with its vertex at the origin is $y^2 = -4ax$, where $a$ is the distance from the vertex to the focus. Given the point $(-2,2)$, substituting $x = -2$ and $y = 2$ into the equation $y^2 = -4ax$ and solving for $a$ gives $a = 0.5$. Thus, the equation simplifies to $y^2 = -2x$, which matches option B.

Write an Equation for the Parabola with Vertex at the Origin