To find the y-value corresponding to the x-value of -1 for the function \( f(x) = 2x^2 - 2x \), we can substitute \(-1\) for \(x\) in the function.
First, substitute \(x = -1\):
\[ f(-1) = 2(-1)^2 - 2(-1) \]
Now, calculate each term:
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Compute \((-1)^2\): \[ (-1)^2 = 1 \]
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Multiply by \(2\): \[ 2 \cdot 1 = 2 \]
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Compute \(-2(-1)\): \[ -2 \cdot -1 = 2 \]
Now, add the results together:
\[ f(-1) = 2 + 2 = 4 \]
Thus, the y-value that corresponds to the x-value of \(-1\) is \( \boxed{4} \).