Precalculus Examples

${(y - 4)}^{2} = - 8 (x + 1)$

Step 1

Isolate $x$ to the left side of the equation.

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Step 1.1

Rewrite the equation as $- 8 (x + 1) = {(y - 4)}^{2}$ .

$- 8 (x + 1) = {(y - 4)}^{2}$

Step 1.2

Divide each term in $- 8 (x + 1) = {(y - 4)}^{2}$ by $- 8$ and simplify.

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Step 1.2.1

Divide each term in $- 8 (x + 1) = {(y - 4)}^{2}$ by $- 8$ .

$\frac{- 8 (x + 1)}{- 8} = \frac{{(y - 4)}^{2}}{- 8}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 8 (x + 1)}{- 8} = \frac{{(y - 4)}^{2}}{- 8}$

Step 1.2.2.1.2

Divide $x + 1$ by $1$ .

$x + 1 = \frac{{(y - 4)}^{2}}{- 8}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$x + 1 = - \frac{{(y - 4)}^{2}}{8}$

Step 1.3

Subtract $1$ from both sides of the equation.

$x = - \frac{{(y - 4)}^{2}}{8} - 1$

Step 1.4

Reorder terms.

$x = - \frac{1}{8} \cdot {(y - 4)}^{2} - 1$

Step 2

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

$a = - \frac{1}{8}$

$h = - 1$

$k = 4$

Step 3

Find the vertex $(h, k)$ .

$(- 1, 4)$

Step 4