To complete the table for the function \( f(x) = 4x^2 \), we will calculate \( f(x) \) for each value of \( x \).
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For \( x = -2 \): \[ f(-2) = 4(-2)^2 = 4 \cdot 4 = 16 \]
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For \( x = -1 \): \[ f(-1) = 4(-1)^2 = 4 \cdot 1 = 4 \]
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For \( x = 0 \): \[ f(0) = 4(0)^2 = 4 \cdot 0 = 0 \]
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For \( x = 1 \): \[ f(1) = 4(1)^2 = 4 \cdot 1 = 4 \]
Now we can fill in the table:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -2 & 16 \ -1 & 4 \ 0 & 0 \ 1 & 4 \ \hline \end{array} \]