Given f, of, x, equals, minus, x, squared, minus, 8f(x)=−x 
2
 −8, find f, of, 4f(4)

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.

Discover how to evaluate the quadratic function f(x) = -x^2 - 8 at x = 4 with a step-by-step solution. This example covers key algebra concepts such as substitution in quadratic functions and simplifying expressions. Ideal for students in Grades 9-10.

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