Find the Parabola with Vertex (-2,4) and Focus (-4,4) (-2,4) , (-4,4)

$(- 2, 4)$ , $(- 4, 4)$

Step 1

Since the $y$ values are the same, use the equation of a parabola that opens left or right.

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

Step 2

Find the distance from the focus to the vertex.

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

$- 4 + 2$

Add $- 4$ and $2$ .

$p = - 2$

Step 3

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

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

Step 4

Multiply $4$ by $- 2$ .

${(y - 4)}^{2} = - 8 (x + 2)$

Step 5