Algebra Examples

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

Step 1

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = \frac{1}{4}$

$h = 2$

$k = 1$

Step 2

Find the vertex $(h, k)$ .

$(2, 1)$

Step 3

Find $p$ , the distance from the vertex to the focus.

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Step 3.1

Find the distance from the vertex to a focus of the parabola by using the following formula.

$\frac{1}{4 a}$

Step 3.2

Substitute the value of $a$ into the formula.

$\frac{1}{4 \cdot \frac{1}{4}}$

Step 3.3

Simplify.

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Step 3.3.1

Combine $4$ and $\frac{1}{4}$ .

$\frac{1}{\frac{4}{4}}$

Step 3.3.2

Simplify by dividing numbers.

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Step 3.3.2.1

Divide $4$ by $4$ .

$\frac{1}{1}$

Step 3.3.2.2

Divide $1$ by $1$ .

$1$

Step 4

Find the directrix.

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Step 4.1

The directrix of a parabola is the horizontal line found by subtracting $p$ from the y-coordinate $k$ of the vertex if the parabola opens up or down.

$y = k - p$

Step 4.2

Substitute the known values of $p$ and $k$ into the formula and simplify.

$y = 0$

Step 5