Choice A is the correct answer. For a parabola opening upward ($a=1$) to be always positive, it must never touch the x-axis. This means no real roots.

1. Discriminant $\Delta < 0$.
2. $k^2 - 4(1)(9) < 0$.
3. $k^2 - 36 < 0$.
4. Roots are $\pm 6$. Test regions: Between -6 and 6 (e.g., $k=0$, $-36 < 0$, True).
5. Range: $-6 < k < 6$.

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