Find the vertex and focus of the parabola. $x ^ { 2 } + 12 y = 0$
A)vertex: (0, 0) focus: $( 0 , - 3 )$
B)vertex: (0, 0) focus: $( 0,3 )$
C)vertex: $( 3,0 )$ focus: (0, 0)
D)vertex: $( - 3,0 )$ focus: (0, 0)
E)vertex: (0, 0) focus: $( 3,0 )$

Question

Quizplus · Accepted Answer

The given equation $x^2 + 12y = 0$ can be rewritten as $x^2 = -12y$, indicating a parabola that opens downwards. The vertex is at the origin (0, 0) because there are no terms to shift the parabola left, right, up, or down. The focus of a parabola is given by $(h, k + \frac{1}{4a})$ for a parabola in the form $x^2 = 4ay$, where $h$ and $k$ are the coordinates of the vertex. Here, $a = -3$, so the focus is $(0, 0 + \frac{1}{4(-3)}) = (0, -3)$.

Find the Vertex and Focus of the Parabola x2+12y=0x ^ { 2 } + 12 y = 0x2+12y=0

Find the Vertex and Focus of the Parabola $x ^ { 2 } + 12 y = 0$