Precalculus Examples

${(y - 2)}^{2} = 4 (x + 3)$

Step 1

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

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Step 1.1

Rewrite the equation as $4 (x + 3) = {(y - 2)}^{2}$ .

$4 (x + 3) = {(y - 2)}^{2}$

Step 1.2

Divide each term in $4 (x + 3) = {(y - 2)}^{2}$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 (x + 3) = {(y - 2)}^{2}$ by $4$ .

$\frac{4 (x + 3)}{4} = \frac{{(y - 2)}^{2}}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 (x + 3)}{4} = \frac{{(y - 2)}^{2}}{4}$

Step 1.2.2.1.2

Divide $x + 3$ by $1$ .

$x + 3 = \frac{{(y - 2)}^{2}}{4}$

Step 1.3

Subtract $3$ from both sides of the equation.

$x = \frac{{(y - 2)}^{2}}{4} - 3$

Step 1.4

Reorder terms.

$x = \frac{1}{4} \cdot {(y - 2)}^{2} - 3$

Step 2

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

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

$h = - 3$

$k = 2$

Step 3

Find the vertex $(h, k)$ .

$(- 3, 2)$

Step 4