Solve the problem.
-The parabola $x ^ { 2 } = - 12 y$ is shifted down 6 units and right 3 units. Find an equation for the new parabola and find the new vertex.
A) $( x - 3 ) ^ { 2 } = - 12 ( y + 6 )$; vertex; $( 3 , - 6 )$
B) $( y + 6 ) ^ { 2 } = - 12 ( x - 3 )$; vertex; $( - 6,3 )$
C) $( x + 6 ) ^ { 2 } = - 12 ( y - 3 )$; vertex; $( - 6,3 )$
D) $( x + 3 ) ^ { 2 } = - 12 ( y - 6 )$; vertex; $( 3 , - 6 )$

Question

Quizplus · Accepted Answer

To shift down 6 units, we need to subtract 6 from y, and to shift right 3 units, we need to subtract 3 from x. This gives us the transformed equation $(x-3)^2=-12(y+6)$. 
To find the vertex, we can rewrite the equation in vertex form, which is $(x-h)^2=4p(y-k)$, where (h,k) is the vertex and p is the distance from the vertex to the focus. 
Comparing this to our transformed equation, we see that $h=3$, $k=-6$, and $4p=-12$, so $p=-3$. Therefore, the vertex is $(3,-6)$.

Solve the Problem x2=−12yx ^ { 2 } = - 12 yx2=−12y

Solve the Problem $x ^ { 2 } = - 12 y$