For what value of k is the line y = 2x + k tangent to the parabola y = x² - 4x + 7?

A line is tangent to a parabola when they meet at exactly one point. Set the expressions equal: $x^2 - 4x + 7 = 2x + k$, which rearranges to $x^2 - 6x + (7 - k) = 0$. One intersection means the discriminant is zero: $(-6)^2 - 4(1)(7 - k) = 0$, so $36 - 28 + 4k = 0$, giving $4k = -8$ and $k = -2$, choice C. Choice A (2) has the wrong sign. Choice B ($-8$) forgets to divide by 4. Choice D (7) is the constant term of the parabola, which has no direct effect on tangency to a line of slope 2.