Find the vertex and focus of the parabola. $x ^ { 2 } + 8 y = 0$
A)vertex: (0,0)focus: (0,-2)
B)vertex: (2,0)focus: (0,0)
C)vertex: (0,0)focus: (-2,0)
D)vertex: (0,0)focus: (0,2)
E)vertex: (-2,0)focus: (0,0)

Question

Find the vertex and focus of the parabola. $x ^ { 2 } + 8 y = 0$ ​
A)vertex: (0,0)focus: (0,-2)
B)vertex: (2,0)focus: (0,0)
C)vertex: (0,0)focus: (-2,0)
D)vertex: (0,0)focus: (0,2)
E)vertex: (-2,0)focus: (0,0)

Quizplus · Accepted Answer

The given equation is $x^2 + 8y = 0$, which can be rewritten as $x^2 = -8y$. This is a parabola that opens downwards. The vertex form of a parabola that opens vertically is $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Comparing, we find $4p = -8$, so $p = -2$. The vertex is at the origin (0,0), and since $p$ is negative, the focus is 2 units below the vertex, at (0, -2).

Find the Vertex and Focus of the Parabola x2+8y=0x ^ { 2 } + 8 y = 0x2+8y=0

Find the Vertex and Focus of the Parabola $x ^ { 2 } + 8 y = 0$