## Respuesta :

**Answer:**

h = -3

Translates the parent function 3 units to the left.

**Step-by-step explanation:**

An** absolute value function**, f(x) = |x - h| + k, is a mathematical function that returns the non-negative magnitude (absolute value) of a real number x. Graphically, it is a **V-shape** with its **vertex **at** (h, k)**, and is **symmetric **about the x-value of its vertex, **x = h**.

As the graph of the given function passes through two points (-6, -2) and (-0, -2) that have the **same y-value** of **y = -2**, and the function is symmetric about the x-value of its vertex, the** value of h** is the **midpoint **of the **x-values** of the **two points**:

[tex]h=\dfrac{-6-0}{2}=\dfrac{-6}{2}=-3[/tex]

We are told that the graph has a vertex at (h, -5), so **k = -5**.

Substituting the **values of h and k** into the given function gives:

[tex]f(x)=|x-(-3)|-5[/tex]

[tex]f(x)=|x+3|-5[/tex]

This is a V-shaped graph, with a vertex at (-3, -5), symmetric about x = -3, and that passes through the points (-6, -2) and (0, -2).

The **absolute value parent function** is f(x) = |x|.

**Adding **"a" to the **x value** of the function **translates **the graph **a units** to the **left**. Therefore, as substituting h = -3 into the formula results in the addition of 3 to the x-value, the graph of the parent function has been translated **3 units to the left**.

**Subtracting k **from the function **translates **the graph** k units down**. Therefore, as k = -5, this value translates the graph of the parent function **5 units down**.