1. **State the problem:** We are given two functions, $f(x)$ and $g(x) = 9(x - 8)^2 - 6$, and we want to compare their minimum values. 2. **Recall the vertex form of a parabola:** A quadratic function in vertex form is $a(x-h)^2 + k$, where $(h,k)$ is the vertex. 3. **Identify the vertex of $g(x)$:** Here, $g(x) = 9(x - 8)^2 - 6$ has vertex at $(8, -6)$. 4. **Minimum value of $g(x)$:** Since $a=9 > 0$, the parabola opens upwards, so the minimum value is the $y$-coordinate of the vertex, which is $-6$. 5. **Minimum value of $f(x)$:** From the graph description, $f(x)$ has a minimum near $x=5$ with minimum value approximately $-8$. 6. **Compare minimum values:** $g(x)$ minimum is $-6$, $f(x)$ minimum is about $-8$. 7. **Conclusion:** Since $-6 > -8$, the minimum value of $g(x)$ is greater than the minimum value of $f(x)$. **Answer:** C. The minimum value of $g(x)$ is greater than the minimum value of $f(x)$.