Algebra Examples

vertex at $(0, - 4)$ and focus at $(0, 1)$

Step 1

Since the $x$ values are the same, use the equation of a parabola that opens up or down.

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

Step 2

Find the distance from the focus to the vertex.

Tap for more steps...

Step 2.1

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

$1 + 4$

Step 2.2

Add $1$ and $4$ .

$p = 5$

Step 3

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

${(x + 0)}^{2} = 4 \cdot 5 (y + 4)$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Add $x$ and $0$ .

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

Step 4.2

Multiply $4$ by $5$ .

$x^{2} = 20 (y + 4)$

Step 5