Precalculus Examples

y = | x + 1 | + 3

$y = | x + 1 | + 3$

Step 1

To find the

x

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

x + 1

$x + 1$ equal to

0

$0$ . In this case,

x + 1 = 0

$x + 1 = 0$ .

x + 1 = 0

$x + 1 = 0$

Step 2

Subtract

1

$1$ from both sides of the equation.

x = - 1

$x = - 1$

Step 3

Replace the variable

x

$x$ with

- 1

$- 1$ in the expression.

y = | (- 1) + 1 | + 3

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

Step 4

Simplify

| (- 1) + 1 | + 3

$| (- 1) + 1 | + 3$ .

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

Add

- 1

$- 1$ and

1

$1$ .

y = | 0 | + 3

$y = | 0 | + 3$

Step 4.1.2

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

0

$0$ and

0

$0$ is

0

$0$ .

y = 0 + 3

$y = 0 + 3$

y = 0 + 3

$y = 0 + 3$

Step 4.2

Add

0

$0$ and

3

$3$ .

y = 3

$y = 3$

y = 3

$y = 3$

Step 5

The absolute value vertex is

(- 1, 3)

$(- 1, 3)$ .

(- 1, 3)

$(- 1, 3)$

Step 6

Enter YOUR Problem