Final answer:
The correct equation of the parabola with a vertex at (4, -3) is x = -3(y + 3)² + 4, which is option D.
Step-by-step explanation:
The equation of a parabola with a vertex at (h, k) can be written in vertex form as y = a(x - h)² + k if the parabola opens upwards or downwards, or as x = a(y - k)² + h if it opens to the left or right. In this case, since the vertex is given as (4, -3), and none of the equations provided are in the form y = a(x - h)² + k, we presume the parabola opens to the left or right, so we expect an equation resembling x = a(y - k)² + h. Thus, the correct equation with the vertex (4, -3) would be x = -3(y + 3)² + 4, which corresponds to option D.