The graph in the image shows a "V" shape that is characteristic of the absolute value function $y = |x|$. However, this graph has been shifted. From observation:

• The vertex of the "V" is located at $(2, 6)$, indicating a horizontal shift of 2 units to the right and a vertical shift of 6 units upward.

The general form of a translated absolute value function is: $y = a |x - h| + k$ where $h$ is the horizontal shift and $k$ is the vertical shift.

Substituting:

• $h = 2$ (right shift),
• $k = 6$ (upward shift).

The equation of the graph is: $y = |x - 2| + 6$

Let me know if you need a detailed step-by-step breakdown!

Expanding Further:

1. How can you identify a function's parent type from its graph?
2. What are the rules for horizontal and vertical translations of functions?
3. How does the slope of the absolute value's arms affect its appearance?
4. What happens when you modify $a$ in the general equation $y = a |x - h| + k$?
5. How can this approach apply to other basic functions, like $x^2$ or $x^3$?

Tip: To confirm transformations, always compare the vertex or origin of the graph to the parent function's location.