Choice A is the correct answer.

1. Set equal: $x^2 = -1$.
2. Since any real number squared is non-negative ($x^2 \geq 0$), there are no real solutions.
3. Geometrically, the parabola opens upward from the origin, and the line $y=-1$ is below it, so they never touch.

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.