Precalculus Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 4$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x + 2$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

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

Step 3

Subtract $2$ from both sides of the equation.

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

Step 4

Reorder terms.

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