Algebra Examples

$\frac{1}{2} (y + 4) = {(x - 7)}^{2}$

Step 1

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

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Step 1.1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (y + 4)) = 2 {(x - 7)}^{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $2 (\frac{1}{2} \cdot (y + 4))$ .

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Step 1.2.1.1

Apply the distributive property.

$2 (\frac{1}{2} y + \frac{1}{2} \cdot 4) = 2 {(x - 7)}^{2}$

Step 1.2.1.2

Combine $\frac{1}{2}$ and $y$ .

$2 (\frac{y}{2} + \frac{1}{2} \cdot 4) = 2 {(x - 7)}^{2}$

Step 1.2.1.3

Cancel the common factor of $2$ .

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Step 1.2.1.3.1

Factor $2$ out of $4$ .

$2 (\frac{y}{2} + \frac{1}{2} \cdot (2 (2))) = 2 {(x - 7)}^{2}$

Step 1.2.1.3.2

Cancel the common factor.

$2 (\frac{y}{2} + \frac{1}{2} \cdot (2 \cdot 2)) = 2 {(x - 7)}^{2}$

Step 1.2.1.3.3

Rewrite the expression.

$2 (\frac{y}{2} + 2) = 2 {(x - 7)}^{2}$

Step 1.2.1.4

Apply the distributive property.

$2 \frac{y}{2} + 2 \cdot 2 = 2 {(x - 7)}^{2}$

Step 1.2.1.5

Cancel the common factor of $2$ .

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Step 1.2.1.5.1

Cancel the common factor.

$2 \frac{y}{2} + 2 \cdot 2 = 2 {(x - 7)}^{2}$

Step 1.2.1.5.2

Rewrite the expression.

$y + 2 \cdot 2 = 2 {(x - 7)}^{2}$

Step 1.2.1.6

Multiply $2$ by $2$ .

$y + 4 = 2 {(x - 7)}^{2}$

Step 1.3

Subtract $4$ from both sides of the equation.

$y = 2 {(x - 7)}^{2} - 4$

Step 2

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

$a = 2$

$h = 7$

$k = - 4$

Step 3

Find the vertex $(h, k)$ .

$(7, - 4)$

Step 4