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Examples

y = | 9 x - 3 |

$y = | 9 x - 3 |$

Step 1

To find the

x

$x$ coordinate of the vertex, set the inside of the absolute value

9 x - 3

$9 x - 3$ equal to

0

$0$ . In this case,

9 x - 3 = 0

$9 x - 3 = 0$ .

9 x - 3 = 0

$9 x - 3 = 0$

Step 2

Solve the equation

9 x - 3 = 0

$9 x - 3 = 0$ to find the

x

$x$ coordinate for the absolute value vertex.

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Step 2.1

Add

3

$3$ to both sides of the equation.

9 x = 3

$9 x = 3$

Step 2.2

Divide each term in

9 x = 3

$9 x = 3$ by

9

$9$ and simplify.

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Step 2.2.1

Divide each term in

9 x = 3

$9 x = 3$ by

9

$9$ .

\frac{9 x}{9} = \frac{3}{9}

$\frac{9 x}{9} = \frac{3}{9}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of

9

$9$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{3}{9}$

Step 2.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{3}{9}$

$x = \frac{3}{9}$

$x = \frac{3}{9}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Cancel the common factor of

$3$ and

$9$ .

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Step 2.2.3.1.1

Factor

$3$ out of

$3$ .

$x = \frac{3 (1)}{9}$

Step 2.2.3.1.2

Cancel the common factors.

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Step 2.2.3.1.2.1

Factor

$3$ out of

$9$ .

$x = \frac{3 \cdot 1}{3 \cdot 3}$

Step 2.2.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 1}{3 \cdot 3}$

Step 2.2.3.1.2.3

Rewrite the expression.

$x = \frac{1}{3}$

$x = \frac{1}{3}$

$x = \frac{1}{3}$

$x = \frac{1}{3}$

$x = \frac{1}{3}$

$x = \frac{1}{3}$

Step 3

Replace the variable

$x$ with

$\frac{1}{3}$ in the expression.

$y = | 9 (\frac{1}{3}) - 3 |$

Step 4

Simplify

$| 9 (\frac{1}{3}) - 3 |$ .

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Step 4.1

Cancel the common factor of

$3$ .

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Step 4.1.1

Factor

$3$ out of

$9$ .

$y = | 3 (3) (\frac{1}{3}) - 3 |$

Step 4.1.2

Cancel the common factor.

$y = | 3 \cdot (3 (\frac{1}{3})) - 3 |$

Step 4.1.3

Rewrite the expression.

$y = | 3 - 3 |$

$y = | 3 - 3 |$

Step 4.2

Subtract

$3$ from

$3$ .

$y = | 0 |$

Step 4.3

The absolute value is the distance between a number and zero. The distance between

$0$ and

$0$ is

$0$ .

$y = 0$

$y = 0$

Step 5

The absolute value vertex is

$(\frac{1}{3}, 0)$ .

$(\frac{1}{3}, 0)$

Step 6

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$