Write the standard form of the equation of the parabola with the given directrix and vertex at (0,0)

A parabola with directrix at implies that the parabola may open 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 up in downward direction.

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

The parabola...

A parabola with directrix at implies that the parabola may open 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 up in downward direction.

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

The parabola indicated in the problem has directrix of which is located below the vertex .

Thus, the parabola opens up in upward direction and follows the standard formula: . We consider the following properties:

vertex as 

focus as 

 directrix as

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

From the given vertex point , we determine and .

Applying directrix and on , we get:

Plug-in the values: , , and  on the standard formula, we get:

 as the standard form of the equation of the parabola with vertex and directrix .