Algebra Examples

$x = 2 \sqrt{3 y}$

Step 1

The domain in terms of $y$ are all the $y$ values that make the radicand non-negative.

$[0, \infty)$

${y | y \geq 0}$

Step 2

To find the radical expression end point, substitute the $y$ value $0$ , which is the least value in the domain, into $f (y) = 2 \sqrt{3 y}$ .

Tap for more steps...

Step 2.1

Replace the variable $y$ with $0$ in the expression.

$f (0) = 2 \sqrt{3 (0)}$

Step 2.2

Simplify the result.

Tap for more steps...

Step 2.2.1

Multiply $3$ by $0$ .

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

Step 2.2.2

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

$f (0) = 2 \sqrt{0^{2}}$

Step 2.2.3

Multiply by zero.

Tap for more steps...

Step 2.2.3.1

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

$f (0) = 2 \cdot 0$

Step 2.2.3.2

Multiply $2$ by $0$ .

$f (0) = 0$

Step 2.2.4

The final answer is $0$ .

$0$

Step 3

The radical expression end point is $(0, 0)$ .

$(0, 0)$

Step 4

Select a few $y$ values from the domain. It would be more useful to select the values so that they are next to the $y$ value of the radical expression end point.

Tap for more steps...

Step 4.1

Substitute the $y$ value $1$ into $2 \sqrt{3 y}$ . In this case, the point is $(3.46, 1)$ .

Tap for more steps...

Step 4.1.1

Replace the variable $y$ with $1$ in the expression.

$f (1) = 2 \sqrt{3 (1)}$

Step 4.1.2

Simplify the result.

Tap for more steps...

Step 4.1.2.1

Multiply $3$ by $1$ .

$f (1) = 2 \sqrt{3}$

Step 4.1.2.2

The final answer is $2 \sqrt{3}$ .

$y = 2 \sqrt{3}$

Step 4.2

Substitute the $y$ value $2$ into $2 \sqrt{3 y}$ . In this case, the point is $(4.9, 2)$ .

Tap for more steps...

Step 4.2.1

Replace the variable $y$ with $2$ in the expression.

$f (2) = 2 \sqrt{3 (2)}$

Step 4.2.2

Simplify the result.

Tap for more steps...

Step 4.2.2.1

Multiply $3$ by $2$ .

$f (2) = 2 \sqrt{6}$

Step 4.2.2.2

The final answer is $2 \sqrt{6}$ .

$y = 2 \sqrt{6}$

Step 4.3

The square root can be graphed using the points around the vertex $(0, 0), (3.46, 1), (4.9, 2)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 3.46 & 1 \\ 4.9 & 2 \end{array}$

Step 5