Algebra Examples

$f (x) = 3 | x |$

Step 1

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

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

Step 2

Find the vertex of $y = 3 | x |$ in order to find $h$ and $k$ .

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Step 2.1

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 2.2

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

$y = 3 | 0 |$

Step 2.3

Simplify $y = 3 | 0 |$ .

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Step 2.3.1

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

$y = 3 \cdot 0$

Step 2.3.2

Multiply $3$ by $0$ .

$y = 0$

Step 2.4

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

$f (x) = (0, 0)$

Step 3

Find $a$ , $h$ , and $k$ , where $a$ is the x coefficient in $y = 3 | x |$ , $h$ is the x-coordinate of the vertex, and $k$ is the y-coordinate of the vertex.

$f (x) = a = 1$

$h = 0$

$k = 0$

Step 4

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

$y = (3) (1) | x - (0) | + 0$

Step 5

Simplify.

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Step 5.1

Remove parentheses.

$y = (3) (1) | x - (0) | + 0$

Step 5.2

Add $(3) (1) | x - (0) |$ and $0$ .

$y = (3) (1) | x - (0) |$

Step 5.3

Multiply $3$ by $1$ .

$y = 3 | x - (0) |$

Step 5.4

Subtract $0$ from $x$ .

$y = 3 | x |$

Step 6