Algebra Examples

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

Step 1

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

$a = - 4$

$h = 0$

$k = 1$

Step 2

Find the vertex $(h, k)$ .

$(0, 1)$

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.

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

Step 3.3

Simplify.

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Step 3.3.1

Multiply $4$ by $- 4$ .

$\frac{1}{- 16}$

Step 3.3.2

Move the negative in front of the fraction.

$- \frac{1}{16}$

Step 4

Find the directrix.

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Step 4.1

The directrix of a parabola is the vertical line found by subtracting $p$ from the x-coordinate $h$ of the vertex if the parabola opens left or right.

$x = h - p$

Step 4.2

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

$x = \frac{1}{16}$

Step 5