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f4

Notice that
y = x^2 + 2kx + k = x^2 + 2kx + k^2 + k - k^2
= (x + k)^2 + k - k^2
Since the axis of symmetry is x + 4 = 0, we have k = 4
and thus it has a global minimum value of
4 - 4^2 = -12

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