Graph Using a Table of Values y = square root of 2x

$y = \sqrt{2 x}$

Step 1

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

$y = \sqrt{2 (- 2)}$

Step 2

Simplify $\sqrt{2 (- 2)}$ .

Multiply $2$ by $- 2$ .

$y = \sqrt{- 4}$

Rewrite $- 4$ as $- 1 (4)$ .

$y = \sqrt{- 1 (4)}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$y = \sqrt{- 1} \cdot \sqrt{4}$

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

$y = i \cdot \sqrt{4}$

Rewrite $4$ as $2^{2}$ .

$y = i \cdot \sqrt{2^{2}}$

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

$y = i \cdot 2$

Move $2$ to the left of $i$ .

$y = 2 i$

Step 3

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

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

Step 4

Simplify $\sqrt{2 (- 1)}$ .

Multiply $2$ by $- 1$ .

$y = \sqrt{- 2}$

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

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

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

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

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

$y = i \sqrt{2}$

Step 5

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

$y = \sqrt{2 (0)}$

Step 6

Simplify $\sqrt{2 (0)}$ .

Multiply $2$ by $0$ .

$y = \sqrt{0}$

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

$y = \sqrt{0^{2}}$

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

$y = 0$

Step 7

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

$y = \sqrt{2 (1)}$

Step 8

Multiply $2$ by $1$ .

$y = \sqrt{2}$

Step 9

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

$y = \sqrt{2 (2)}$

Step 10

Simplify $\sqrt{2 (2)}$ .

Multiply $2$ by $2$ .

$y = \sqrt{4}$

Rewrite $4$ as $2^{2}$ .

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

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

$y = 2$

Step 11

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

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

Step 12

Graph Using a Table of Values y = square root of 2x

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