1. **State the problem:** We are given a V-shaped absolute value graph with vertex at $(-4, 2)$ opening upwards. We need to find the equation of the function in the form $a|x - h| + k$ where $a$, $h$, and $k$ are integers or simplified fractions. 2. **Recall the formula:** The general form of an absolute value function is: $$y = a|x - h| + k$$ where $(h, k)$ is the vertex and $a$ controls the slope (steepness) and direction (up or down). 3. **Identify vertex:** From the graph, vertex is at $(-4, 2)$, so $h = -4$ and $k = 2$. 4. **Find $a$ using another point:** Choose a point on the graph other than the vertex. For example, the point $(0, 6)$ lies on the graph. 5. **Plug values into the formula:** $$6 = a|0 - (-4)| + 2$$ $$6 = a|4| + 2$$ $$6 = 4a + 2$$ 6. **Solve for $a$:** $$6 - 2 = 4a$$ $$4 = 4a$$ $$a = \frac{4}{4} = 1$$ 7. **Write the final equation:** $$y = 1|x - (-4)| + 2 = |x + 4| + 2$$ **Answer:** $$y = |x + 4| + 2$$