Find the Parabola with Vertex (0,3) and Directrix y=-3 (0,3) y=-3

$(0, 3)$ $y = - 3$

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 $p$ .

$p = 3 + 3$

Add $3$ and $3$ .

$p = 6$

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

${(x - 0)}^{2} = 4 (6) (y - 3)$

Simplify.

$x^{2} = 24 (y - 3)$

Find the Parabola with Vertex (0,3) and Directrix y=-3 (0,3) y=-3

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