Precalculus Examples

$y = 4 | x | + 1$

Step 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

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

$y = 4 | 0 | + 1$

Step 3

Simplify $4 | 0 | + 1$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

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

$y = 4 \cdot 0 + 1$

Step 3.1.2

Multiply $4$ by $0$ .

$y = 0 + 1$

Step 3.2

Add $0$ and $1$ .

$y = 1$

Step 4

The absolute value vertex is $(0, 1)$ .

$(0, 1)$

Step 5