1. The problem asks for the vertex of the graph of the function $f(x+3)$. 2. The vertex of a function $f(x)$ is the point where the graph changes direction, often given as $(h, k)$ for a vertex form $f(x) = a(x-h)^2 + k$. 3. If the original function $f(x)$ has a vertex at $(h, k)$, then the function $f(x+3)$ shifts the graph horizontally by $-3$ units (to the left). 4. From the description, the original vertex is near $(-2, 5)$ because shifting $x$ by $+3$ moves the vertex left by 3 units, so the original vertex before shifting is at $(-2, 5)$. 5. Therefore, the vertex of $f(x+3)$ is at $(-2 - 3, 5) = (-5, 5)$. 6. However, the options given are: A. $(-8, 5)$ B. $(-5, 2)$ C. $(-5, 8)$ D. $(-2, 5)$ 7. Since the vertex is near $(-5, 5)$ and the closest option with $x = -5$ is either B or C, we check the $y$ values. The graph vertex is between 0 and 10, closer to 5, so $y=8$ or $y=2$ are options. 8. The description says the vertex is below and to the left of the y-axis near $x=-5$ and $y$ between 0 and 10, with an arrow pointing downward from around $y=10$ towards the curve, suggesting the vertex is lower than 10 but not very low. 9. The best match is option C: $(-5, 8)$. Final answer: C. $(-5, 8)$