Find the Parabola with Vertex (0,0) and Focus (0,2) (0,0) , (0,2)

$(0, 0) (0, 2)$

Since the $x$ values are the same, 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.

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

$p = 2 - 0$

Subtract $0$ from $2$ .

$p = 2$

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 Focus (0,2) (0,0) , (0,2)

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