To solve $f(7)$ for the function $f(x) = -x^2 + 6x - 9$, we need to substitute $x = 7$ into the function and simplify:

$f(7) = -(7)^2 + 6 \cdot 7 - 9$

Calculating each part:

1. $-(7)^2 = -49$
2. $6 \cdot 7 = 42$
3. Combining these values: $-49 + 42 - 9$

Now, simplify:

$-49 + 42 = -7$ $-7 - 9 = -16$

So, $f(7) = -16$.

Would you like further details on the steps? Here are some related questions for further exploration:

1. What is the general form of a quadratic function, and how do we analyze it?
2. How can we find the maximum or minimum of a quadratic function?
3. What is the significance of the negative coefficient of $x^2$ in this function?
4. How would we determine the vertex of this quadratic function?
5. Can we find the roots of $f(x) = 0$ for this function?

Tip: When evaluating functions at a specific point, substituting carefully and simplifying in steps can help reduce errors.