Algebra Examples

$y = \frac{1}{2} \sqrt{x}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt{- 2}$

Step 2

Simplify $\frac{1}{2} \cdot \sqrt{- 2}$ .

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Step 2.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt{- 2}$

Step 2.2

Rewrite $- 2$ as $- 1 (2)$ .

$y = \frac{1}{2} \cdot \sqrt{- 1 (2)}$

Step 2.3

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$y = \frac{1}{2} \cdot (\sqrt{- 1} \cdot \sqrt{2})$

Step 2.4

Rewrite $\sqrt{- 1}$ as $i$ .

$y = \frac{1}{2} \cdot (i \cdot \sqrt{2})$

Step 2.5

Multiply $\frac{1}{2} (i \sqrt{2})$ .

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Step 2.5.1

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

$y = \frac{i}{2} \sqrt{2}$

Step 2.5.2

Combine $\frac{i}{2}$ and $\sqrt{2}$ .

$y = \frac{i \sqrt{2}}{2}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt{- 1}$

Step 4

Simplify $\frac{1}{2} \cdot \sqrt{- 1}$ .

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Step 4.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt{- 1}$

Step 4.2

Rewrite $\sqrt{- 1}$ as $i$ .

$y = \frac{1}{2} \cdot i$

Step 4.3

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

$y = \frac{i}{2}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt{0}$

Step 6

Simplify $\frac{1}{2} \cdot \sqrt{0}$ .

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Step 6.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt{0}$

Step 6.2

Rewrite $0$ as $0^{2}$ .

$y = \frac{1}{2} \cdot \sqrt{0^{2}}$

Step 6.3

Pull terms out from under the radical, assuming positive real numbers.

$y = \frac{1}{2} \cdot 0$

Step 6.4

Multiply $\frac{1}{2}$ by $0$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt{1}$

Step 8

Simplify $\frac{1}{2} \cdot \sqrt{1}$ .

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Step 8.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt{1}$

Step 8.2

Any root of $1$ is $1$ .

$y = \frac{1}{2} \cdot 1$

Step 8.3

Multiply $\frac{1}{2}$ by $1$ .

$y = \frac{1}{2}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt{2}$

Step 10

Simplify $\frac{1}{2} \cdot \sqrt{2}$ .

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Step 10.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt{2}$

Step 10.2

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

$y = \frac{\sqrt{2}}{2}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & \frac{i \sqrt{2}}{2} \\ - 1 & \frac{i}{2} \\ 0 & 0 \\ 1 & \frac{1}{2} \\ 2 & \frac{\sqrt{2}}{2} \end{array}$

Step 12