To find $f(-7)$ for the function $f(x) = -x^2 - 4x - 12$, follow these steps:

1. Substitute $x = -7$ into the function.

   $f(-7) = -(-7)^2 - 4(-7) - 12$

2. Calculate each term:

   • First, $(-7)^2 = 49$.
   • Then, $-49 = -49$.
   • For $-4(-7)$, multiply to get $+28$.

3. Substitute these values into the expression:

   $f(-7) = -49 + 28 - 12$

4. Simplify:

   $f(-7) = -49 + 28 - 12 = -33$

So, $f(-7) = -33$.

Would you like more details, or do you have any questions?

Here are some related questions for further practice:

1. How would you find $f(2)$ for the same function?
2. Can you find the x-intercepts of $f(x) = -x^2 - 4x - 12$?
3. What is the vertex of the parabola represented by $f(x) = -x^2 - 4x - 12$?
4. How do you determine if $f(x)$ has a maximum or minimum value?
5. What is the range of the function $f(x) = -x^2 - 4x - 12$?

Tip: When working with functions, substituting negative values can lead to sign changes in the terms. Be cautious with squares and negative signs.