The focus of a parabola is located at (4,0), and the directrix is located at x = –4.

The vertex lies halfway between the focus at (4, 0) and the directrix x = −4, so it is at (0, 0). The distance from the vertex to the focus is p = 4, and the parabola opens to the right. A horizontal parabola with vertex at the origin has equation y² = 4px, giving y² = 16x. Therefore, the correct choice is D, y² = 16x.

AI-written and checked against the verified answer.