Set 17: Quadratic Equations (Advanced)

Choice A is correct. Choice A is the correct answer. A line is tangent to a parabola if they intersect at exactly one point. 1. Set equal: $x^2 = 2 x + k$. 2. Rearrange: $x^2 - 2 x - k = 0$. 3. Set discriminant to 0: $\Delta = (-2)^2 - 4(1)(-k) = 0$. 4. $4+ 4 k = 0 \Rightarrow 4 k = -4 \Rightarrow k = -1$. Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.