Algebra Examples

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

Step 1

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

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

Step 2

Find the distance from the focus to the vertex.

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Step 2.1

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 $p$ .

$p = 3 + 3$

Step 2.2

Add $3$ and $3$ .

$p = 6$

Step 3

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

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

Step 4

Simplify.

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

Step 5