Find the Parabola with Vertex (0,0) and Focus (-8,0) (0,0) , (-8,0)

$(0, 0)$ , $(- 8, 0)$

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 $p$ .

$- 8 - 0$

Subtract $0$ from $- 8$ .

$p = - 8$

Step 3

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

${(y + 0)}^{2} = 4 \cdot - 8 (x + 0)$

Step 4

Simplify.

Add $y$ and $0$ .

$y^{2} = 4 \cdot - 8 (x + 0)$

Multiply $4$ by $- 8$ .

$y^{2} = - 32 (x + 0)$

Add $x$ and $0$ .

$y^{2} = - 32 x$

Step 5