Find the Parabola with Vertex (-4,0) and Directrix x=4 vertex (-4,0) directrix x=4

vertex $(- 4, 0)$ directrix $x = 4$

Since the directrix is horizontal, use the equation of a parabola that opens left or right.

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

Find the distance from the focus to the vertex.

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 $x$ coordinate of the vertex to find $p$ .

$p = - 4 - 4$

Subtract $4$ from $- 4$ .

$p = - 8$

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

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

Simplify.

$y^{2} = - 32 (x + 4)$

Find the Parabola with Vertex (-4,0) and Directrix x=4 vertex (-4,0) directrix x=4

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