Absolute Value Graph 217D6C

1. The problem is to find the equation of an absolute value graph with vertex at $(-3, -4)$ and passing through $(-2, -3)$. 2. The general form of an absolute value function with vertex $(h, k)$ is: $$y = a|x - h| + k$$ where $a$ controls the slope of the arms and the direction of opening. 3. Since the vertex is at $(-3, -4)$, substitute $h = -3$ and $k = -4$: $$y = a|x + 3| - 4$$ 4. Use the point $(-2, -3)$ to find $a$: $$-3 = a|-2 + 3| - 4$$ $$-3 = a|1| - 4$$ $$-3 = a - 4$$ 5. Solve for $a$: $$a = -3 + 4 = 1$$ 6. Therefore, the equation is: $$y = |x + 3| - 4$$ This matches the graph's vertex and the point given, and the graph opens upward because $a = 1 > 0$.