Finite Math Examples

| x | = 2

$| x | = 2$

Step 1

Rewrite

| x | = 2

$| x | = 2$ as

y = | x | - 2

$y = | x | - 2$ .

y = | x | - 2

$y = | x | - 2$

Step 2

The standard form for an absolute value equation is

y = a | x - h | + k

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

y = a | x - h | + k

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

Step 3

Find the vertex of

y = | x | - 2

$y = | x | - 2$ in order to find

h

$h$ and

k

$k$ .

Tap for more steps...

Step 3.1

To find the

x

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

x

$x$ equal to

0

$0$ . In this case,

x = 0

$x = 0$ .

x = 0

$x = 0$

Step 3.2

Replace the variable

x

$x$ with

0

$0$ in the expression.

y = | 0 | - 2

$y = | 0 | - 2$

Step 3.3

Simplify

y = | 0 | - 2

$y = | 0 | - 2$ .

Tap for more steps...

Step 3.3.1

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

0

$0$ and

0

$0$ is

0

$0$ .

y = 0 - 2

$y = 0 - 2$

Step 3.3.2

Subtract

2

$2$ from

0

$0$ .

y = - 2

$y = - 2$

y = - 2

$y = - 2$

Step 3.4

The absolute value vertex is

(0, - 2)

$(0, - 2)$ .

(0, - 2)

$(0, - 2)$

(0, - 2)

$(0, - 2)$

Step 4

Find

a

$a$ ,

h

$h$ , and

k

$k$ , where

a

$a$ is the x coefficient in

y = | x | - 2

$y = | x | - 2$ ,

h

$h$ is the x-coordinate of the vertex, and

k

$k$ is the y-coordinate of the vertex.

a = 1

$a = 1$

h = 0

$h = 0$

k = - 2

$k = - 2$

Step 5

Substitute the

a

$a$ ,

h

$h$ , and

k

$k$ values into the standard form equation,

y = a | x - h | + k

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

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

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

Step 6

Simplify.

Tap for more steps...

Step 6.1

Remove parentheses.

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

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

Step 6.2

Simplify each term.

Tap for more steps...

Step 6.2.1

Multiply

| x - (0) |

$| x - (0) |$ by

1

$1$ .

y = | x - (0) | - 2

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

Step 6.2.2

Subtract

0

$0$ from

x

$x$ .

y = | x | - 2

$y = | x | - 2$

y = | x | - 2

$y = | x | - 2$

y = | x | - 2

$y = | x | - 2$

Step 7