Precalculus Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

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.

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

Step 1.2.2.1.2

Divide $y - 2$ by $1$ .

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

Step 1.3

Add $2$ to both sides of the equation.

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

Step 1.4

Reorder terms.

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

Step 2

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

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

$h = 1$

$k = 2$

Step 3

Find the vertex $(h, k)$ .

$(1, 2)$

Step 4