Precalculus Examples

$y = 2 | - x - 3 | + 5$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $- x - 3$ equal to $0$ . In this case, $- x - 3 = 0$ .

$- x - 3 = 0$

Step 2

Solve the equation $- x - 3 = 0$ to find the $x$ coordinate for the absolute value vertex.

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Step 2.1

Add $3$ to both sides of the equation.

$- x = 3$

Step 2.2

Divide each term in $- x = 3$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Step 2.2.2.2

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $3$ by $- 1$ .

$x = - 3$

Step 3

Replace the variable $x$ with $- 3$ in the expression.

$y = 2 | - (- 3) - 3 | + 5$

Step 4

Simplify $2 | - (- 3) - 3 | + 5$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $- 1$ by $- 3$ .

$y = 2 | 3 - 3 | + 5$

Step 4.1.2

Subtract $3$ from $3$ .

$y = 2 | 0 | + 5$

Step 4.1.3

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

$y = 2 \cdot 0 + 5$

Step 4.1.4

Multiply $2$ by $0$ .

$y = 0 + 5$

Step 4.2

Add $0$ and $5$ .

$y = 5$

Step 5

The absolute value vertex is $(- 3, 5)$ .

$(- 3, 5)$

Step 6