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 $f(x)$?
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3. How would you sketch the graph of $f(x)$?
4. What is the vertex of the parabola described by $f(x)$?
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Tip: Always double-check your substitutions and simplifications when dealing with functions to avoid common algebraic errors.