To find the y-value that corresponds to the x-value of -1 for the function \( f(x) = 2x^2 - 2x \), we need to substitute -1 into the function.
Calculate \( f(-1) \):
\[ f(-1) = 2(-1)^2 - 2(-1) \]
First, calculate \( (-1)^2 \):
\[ (-1)^2 = 1 \]
Now substitute this back into the function:
\[ f(-1) = 2(1) - 2(-1) \] \[ = 2 - (-2) \] \[ = 2 + 2 \] \[ = 4 \]
Thus, the y-value that corresponds to the x-value of -1 is \( 4 \).