Precalculus Examples

$y = \frac{3}{4} | x + 3 | - 6$

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

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 3

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

$y = \frac{3}{4} \cdot | (- 3) + 3 | - 6$

Step 4

Simplify $\frac{3}{4} \cdot | (- 3) + 3 | - 6$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

Add $- 3$ and $3$ .

$y = \frac{3}{4} \cdot | 0 | - 6$

Step 4.1.2

Remove non-negative terms from the absolute value.

$y = \frac{3}{4} \cdot 0 - 6$

Step 4.1.3

Multiply $\frac{3}{4}$ by $0$ .

$y = 0 - 6$

Step 4.2

Subtract $6$ from $0$ .

$y = - 6$

Step 5

The absolute value vertex is $(- 3, - 6)$ .

$(- 3, - 6)$

Step 6