Algebra Examples

vertex at

(0, - 4)

$(0, - 4)$ and focus at

(0, 1)

$(0, 1)$

Step 1

Since the

x

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

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

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

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 |

$| p |$ . Subtract the

y

$y$ coordinate of the vertex from the

y

$y$ coordinate of the focus to find

p

$p$ .

1 + 4

$1 + 4$

Step 2.2

Add

1

$1$ and

4

$4$ .

p = 5

$p = 5$

p = 5

$p = 5$

Step 3

Substitute the known values for the variables into the equation

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

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

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

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

Step 4

Simplify.

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Step 4.1

Add

x

$x$ and

0

$0$ .

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

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

Step 4.2

Multiply

4

$4$ by

5

$5$ .

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

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

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

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

Step 5