Finite Math Examples

$| x | = 2$

Step 1

Rewrite $| x | = 2$ as $y = | x | - 2$ .

$y = | x | - 2$

Step 2

The standard form for an absolute value equation is $y = a | x - h | + k$ .

$y = a | x - h | + k$

Step 3

Find the vertex of $y = | x | - 2$ in order to find $h$ and $k$ .

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Step 3.1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x$ equal to $0$ . In this case, $x = 0$ .

$x = 0$

Step 3.2

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

$y = | 0 | - 2$

Step 3.3

Simplify $y = | 0 | - 2$ .

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Step 3.3.1

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$y = 0 - 2$

Step 3.3.2

Subtract $2$ from $0$ .

$y = - 2$

Step 3.4

The absolute value vertex is $(0, - 2)$ .

$(0, - 2)$

Step 4

Find $a$ , $h$ , and $k$ , where $a$ is the x coefficient in $y = | x | - 2$ , $h$ is the x-coordinate of the vertex, and $k$ is the y-coordinate of the vertex.

$a = 1$

$h = 0$

$k = - 2$

Step 5

Substitute the $a$ , $h$ , and $k$ values into the standard form equation, $y = a | x - h | + k$ .

$y = (1) | x - (0) | - 2$

Step 6

Simplify.

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Step 6.1

Remove parentheses.

$y = (1) | x - (0) | - 2$

Step 6.2

Simplify each term.

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Step 6.2.1

Multiply $| x - (0) |$ by $1$ .

$y = | x - (0) | - 2$

Step 6.2.2

Subtract $0$ from $x$ .

$y = | x | - 2$

Step 7