Find the Parabola with Vertex (-2,4) and Directrix x=-1 The vertex is (-2,4) ; the directrix is x=-1

The vertex is $(- 2, 4)$ ; the directrix is $x = - 1$

Step 1

Since the directrix is horizontal, 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 and from the vertex to the directrix is $| p |$ . Subtract the value of the directrix from the $x$ coordinate of the vertex to find $p$ .

$p = - 2 + 1$

Add $- 2$ and $1$ .

$p = - 1$

Step 3

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

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

Step 4

Simplify.

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

Step 5

Find the Parabola with Vertex (-2,4) and Directrix x=-1 The vertex is (-2,4) ; the directrix is x=-1

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