Calculus Examples

$x - y^{2} = 0$

Step 1

Subtract $x$ from both sides of the equation.

$- y^{2} = - x$

Step 2

Divide each term in $- y^{2} = - x$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- y^{2} = - x$ by $- 1$ .

$\frac{- y^{2}}{- 1} = \frac{- x}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{y^{2}}{1} = \frac{- x}{- 1}$

Step 2.2.2

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{- x}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Dividing two negative values results in a positive value.

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

Step 2.3.2

Divide $x$ by $1$ .

$y^{2} = x$

Step 3

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

$y = \pm \sqrt{x}$

Step 4

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

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Step 4.1

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

$y = \sqrt{x}$

Step 4.2

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

$y = - \sqrt{x}$

Step 4.3

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

$y = \sqrt{x}$

$y = - \sqrt{x}$

$y = \sqrt{x}$

$y = - \sqrt{x}$

Step 5

Set the radicand in $\sqrt{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

Step 6

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 7