The graph you've shared shows a V-shaped graph, which is a characteristic of an absolute value function. The vertex of the graph is at the point (-4, 0), indicating a horizontal shift of 4 units to the left from the origin.

Among the given options, let's analyze each one:

1. $y = |x| + 4$: This represents a standard absolute value function shifted 4 units up. This does not match the graph because the graph is not shifted upward.

2. $y = |x + 4|$: This is an absolute value function shifted 4 units to the left, which fits the graph's vertex at (-4, 0). This seems to be the correct equation.

3. $y = |x| - 4$: This would shift the graph 4 units down, which does not match.

4. $y = |x - 4|$: This would shift the graph 4 units to the right, but the vertex is at (-4, 0), so this is not correct.

Thus, the correct equation that matches the graph is: $y = |x + 4|$

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. How would the graph change if the equation were $y = |x - 3|$?
2. What happens to the graph of $y = |x + 4|$ if you add a constant inside the absolute value?
3. How do you determine the vertex of the function $y = |x + a|$?
4. What transformation does the function $y = -|x|$ represent?
5. How can you graph the function $y = |x + 2| - 3$?

Tip: The expression inside the absolute value, $x + c$, controls horizontal shifts, while constants outside control vertical shifts!