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You want to evaluate \( f(x - 2) \) given that \( f(x) = -3x^2 - 4x - 4 \).

To find \( f(x - 2) \), we substitute \( x - 2 \) for \( x \) in the function:
\[
f(x - 2) = -3(x - 2)^2 - 4(x - 2) - 4
\]

Expanding and simplifying the expression:
\[
(x - 2)^2 = x^2 - 4x + 4
\]
\[
-3(x^2 - 4x + 4) = -3x^2 + 12x - 12
\]
\[
-4(x - 2) = -4x + 8
\]
\[
f(x - 2) = -3x^2 + 12x - 12 - 4x + 8 - 4 = -3x^2 + 8x - 8
\]

Thus, \( f(x - 2) = -3x^2 + 8x - 8 \).

Would you like to know more details about any step in this solution or have other questions?

Here are some related questions you might consider:
1. How do you find the derivative of \( f(x) \)?
2. What are the roots of the function \( f(x) \)?
3. How would you sketch the graph of \( f(x) \)?
4. What is the vertex of the parabola described by \( f(x) \)?
5. How do you integrate the function \( f(x) \)?

**Tip:** Always double-check your substitutions and simplifications when dealing with functions to avoid common algebraic errors.

Evaluate f(x - 2) when f(x) = -3x^2 - 4x - 4.

Learn how to evaluate f(x - 2) when f(x) = -3x^2 - 4x - 4 by using function substitution and quadratic expansion. This step-by-step solution is perfect for high school students studying algebra and quadratic functions.

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