A parabola with directrix at `y=k` implies that the parabola may opens up towards upward or downward direction.

The position of the directrix with respect to the vertex point can be used to determine in which side the parabola opens up.

If the directrix is above the vertex point then the parabola opens downward.

If the directrix is below the vertex point then the parabola opens upward.

The parabola indicated in the problem has directrix of `y=12` which is located above the vertex `(0,0)` .

Thus, the **parabola opens downward** and follows the standard
formula: `(x-h)^2=-4p(y-k)` . We consider the following properties:

vertex as `(h,k)`

focus as `(h, k-p)`

directrix as `y=k+p`

Note: `p` is the distance of between focus and vertex or distance between directrix and vertex.

From the given vertex point `(0,0)` , we determine `h =0` and `k=0` .

Applying directrix `y =12` and `k=0` on `y=k+p` we get:

`12 =0+p`

`12=p or p=12` .

Plug-in the values: `h=0` ,`k=0` , and `p=7` on the standard formula, we get:

` (x-0)^2=-4*12(y-0)`

`x^2=-48y` as the **standard form of the equation of the
parabola** with vertex `(0,0)` and directrix `y=12.`

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.