Algebra Examples

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

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

Step 1

Substitute

- 2

$- 2$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 2

Simplify

\frac{1}{2} \cdot \sqrt{- 2}

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

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Step 2.1

Remove parentheses.

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

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

Step 2.2

Rewrite

- 2

$- 2$ as

- 1 (2)

$- 1 (2)$ .

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

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

Step 2.3

Rewrite

\sqrt{- 1 (2)}

$\sqrt{- 1 (2)}$ as

\sqrt{- 1} \cdot \sqrt{2}

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

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

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

Step 2.4

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

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

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

Step 2.5

Multiply

\frac{1}{2} (i \sqrt{2})

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

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Step 2.5.1

Combine

i

$i$ and

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 2.5.2

Combine

\frac{i}{2}

$\frac{i}{2}$ and

\sqrt{2}

$\sqrt{2}$ .

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

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

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

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

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

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

Step 3

Substitute

- 1

$- 1$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 4

Simplify

\frac{1}{2} \cdot \sqrt{- 1}

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

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Step 4.1

Remove parentheses.

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

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

Step 4.2

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

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

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

Step 4.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

i

$i$ .

y = \frac{i}{2}

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

y = \frac{i}{2}

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

Step 5

Substitute

0

$0$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 6

Simplify

\frac{1}{2} \cdot \sqrt{0}

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

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Step 6.1

Remove parentheses.

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

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

Step 6.2

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

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

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

Step 6.4

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

0

$0$ .

y = 0

$y = 0$

y = 0

$y = 0$

Step 7

Substitute

1

$1$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 8

Simplify

\frac{1}{2} \cdot \sqrt{1}

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

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Step 8.1

Remove parentheses.

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

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

Step 8.2

Any root of

1

$1$ is

1

$1$ .

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

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

Step 8.3

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

1

$1$ .

y = \frac{1}{2}

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

y = \frac{1}{2}

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

Step 9

Substitute

2

$2$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 10

Simplify

\frac{1}{2} \cdot \sqrt{2}

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

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Step 10.1

Remove parentheses.

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

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

Step 10.2

Combine

\frac{1}{2}

$\frac{1}{2}$ and

\sqrt{2}

$\sqrt{2}$ .

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

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

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

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

Step 12