Find the Parabola with Vertex (-2,2) and Focus (-2,3) (-2,3) , (-2,2)

$(- 2, 3)$ , $(- 2, 2)$

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 $p$ .

$3 - 2$

Subtract $2$ from $3$ .

$p = 1$

Step 3

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

${(x + 2)}^{2} = 4 \cdot 1 (y - 2)$

Step 4

Multiply $4$ by $1$ .

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

Step 5