# How do you find the standard form of the equation of the parabola with Vertex at the origin, focus at (0, -4)?

Nov 22, 2016

${x}^{2} = - 16 y$

#### Explanation:

graph{x^2=-16y [-10, 10, -5, 5]} The vector $V S$ joining the vertex

V(0, 0) and the focus, down at S(0, -4), designates the axis of the

parabola.

So, the axis is y-axis, in the negative direction...

The size of the parabola is VS = a = 4.

Easily, the equation is ${x}^{2} = - 4 a y = - 16 y$. See the graph.