The given function is $f(x) = -x^2 - 8$. You are asked to find $f(4)$.

Step-by-step solution:

1. The function is $f(x) = -x^2 - 8$.
2. Plug $x = 4$ into the function: $f(4) = -(4)^2 - 8$
3. Simplify: $f(4) = -16 - 8$ $f(4) = -24$

Thus, $f(4) = -24$.

Answer:

$f(4) = -24$.

Do you want any more details or have any questions?

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Here are 5 related questions to explore further:

1. What is the value of $f(-4)$ for the same function?
2. How would the function change if the equation was $f(x) = -x^2 + 8$?
3. What is the vertex of the parabola described by $f(x) = -x^2 - 8$?
4. Find the domain and range of the function $f(x) = -x^2 - 8$.
5. What is the axis of symmetry for the function $f(x) = -x^2 - 8$?

Tip: For quadratic functions like $f(x) = -x^2 - 8$, the negative sign before $x^2$ indicates the parabola opens downwards.