The problem is asking to evaluate the function $g(x) = -x^2 + 6x + 1$ at $x = -3$.

Step-by-Step Solution:

1. Start with the given function: $g(x) = -x^2 + 6x + 1$

2. Substitute $x = -3$ into the equation: $g(-3) = -(-3)^2 + 6(-3) + 1$

3. Simplify each term:

   • $(-3)^2 = 9$, so the first term becomes $-9$
   • The second term is $6(-3) = -18$
   • The third term remains as $+1$

   Therefore, the expression becomes: $g(-3) = -9 - 18 + 1$

4. Add the terms: $g(-3) = -9 - 18 + 1 = -26$

Final Answer:

$g(-3) = -26$

Would you like further clarification on this solution? Here are 5 related questions you could explore:

1. How does substituting different values into the function affect the result?
2. What are the key characteristics of a quadratic function like $g(x) = -x^2 + 6x + 1$?
3. How would you graph the function $g(x) = -x^2 + 6x + 1$?
4. How do you find the vertex of the quadratic function $g(x)$?
5. What does the negative sign in front of $x^2$ signify in terms of the graph's shape?

Tip: When working with quadratic functions, always simplify carefully after substituting values to avoid mistakes!