Graph Using a Table of Values y^2+x=2

$y^{2} + x = 2$

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

$y^{2} - 2 = 2$

Solve the equation for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Add $2$ to both sides of the equation.

$y^{2} = 2 + 2$

Add $2$ and $2$ .

$y^{2} = 4$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

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

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

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

$y = \pm 2$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$y = 2, - 2$

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

$y^{2} - 1 = 2$

Solve the equation for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Add $1$ to both sides of the equation.

$y^{2} = 2 + 1$

Add $2$ and $1$ .

$y^{2} = 3$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{3}, - \sqrt{3}$

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

$y^{2} + 0 = 2$

Solve the equation for $y$ .

Add $y^{2}$ and $0$ .

$y^{2} = 2$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{2}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{2}, - \sqrt{2}$

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

$y^{2} + 1 = 2$

Solve the equation for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$y^{2} = 2 - 1$

Subtract $1$ from $2$ .

$y^{2} = 1$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$y = \pm 1$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = 1$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 1$

The complete solution is the result of both the positive and negative portions of the solution.

$y = 1, - 1$

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

$y^{2} + 2 = 2$

Solve the equation for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$y^{2} = 2 - 2$

Subtract $2$ from $2$ .

$y^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

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

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

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

$y = \pm 0$

Plus or minus $0$ is $0$ .

$y = 0$

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

$\begin{array}{c} x & y \\ - 2 & 2 \\ - 1 & - 2 \\ 0 & \sqrt{3} \\ 1 & - \sqrt{3} \\ 2 & \sqrt{2} \end{array}$

Graph Using a Table of Values y^2+x=2

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