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

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

Step 1

Since the $x$ values are the same, use the equation of a parabola that opens up or down.

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

Step 2

Find the distance from the focus to the vertex.

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 $p$ .

$2 - 0$

Subtract $0$ from $2$ .

$p = 2$

Step 3

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

${(x + 0)}^{2} = 4 \cdot 2 (y + 0)$

Step 4

Simplify.

Add $x$ and $0$ .

$x^{2} = 4 \cdot 2 (y + 0)$

Multiply $4$ by $2$ .

$x^{2} = 8 (y + 0)$

Add $y$ and $0$ .

$x^{2} = 8 y$

Step 5