Algebra Examples

$(3, - 1)$ , $(- 2, - 1)$

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.

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Step 2.1

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 $p$ .

$- 2 - 3$

Step 2.2

Subtract $3$ from $- 2$ .

$p = - 5$

Step 3

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

${(y + 1)}^{2} = 4 \cdot - 5 (x - 3)$

Step 4

Multiply $4$ by $- 5$ .

${(y + 1)}^{2} = - 20 (x - 3)$

Step 5