Write an equation for the parabola with vertex at the origin.
-Through $( 3 , - 6 )$, opening downward
A) $x ^ { 2 } = - \frac { 3 } { 2 } y$
B) $x ^ { 2 } = - \frac { 2 } { 3 }$
C) $y = \frac { 2 } { 3 } x ^ { 2 }$
D) $x = - \frac { 2 } { 3 } y ^ { 2 }$

Question

Quizplus · Accepted Answer

The equation for a parabola with its vertex at the origin and opening downward is $y = -ax^2$. Substituting the point (3, -6) into the equation gives $-6 = -a(3)^2$, solving for $a$ gives $a = \frac{2}{3}$, thus the correct equation is $y = -\frac{2}{3}x^2$, which can be rearranged to $x^2 = -\frac{3}{2}y$, matching option A.

Write an Equation for the Parabola with Vertex at the Origin