Find the Parabola with Vertex (0,0) and Directrix y=-2 Vertex (0,0) ; directrix y=-2

Vertex $(0, 0)$ ; directrix $y = - 2$

Since the directrix is vertical, use the equation of a parabola that opens up or down.

${(x - h)}^{2} = 4 p (y - k)$

Find the distance from the focus to the vertex.

The distance from the focus to the vertex and from the vertex to the directrix is $| p |$ . Subtract the value of the directrix from the $y$ coordinate of the vertex to find $p$ .

$p = 0 + 2$

Add $0$ and $2$ .

$p = 2$

Substitute in the known values for the variables into the equation ${(x - h)}^{2} = 4 p (y - k)$ .

${(x - 0)}^{2} = 4 (2) (y - 0)$

Simplify.

$x^{2} = 8 y$

Find the Parabola with Vertex (0,0) and Directrix y=-2 Vertex (0,0) ; directrix y=-2

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