Final answer:
The problem is about finding the equation of a parabola with a given vertex and a point it contains, considering the line of symmetry is horizontal y = -8.
Step-by-step explanation:
The student is dealing with a geometry problem that involves understanding the properties of a parabola. The question at hand describes a vertex of a parabola and a line of symmetry, which gives us clues to use for the formulation of the equation of the parabola. Given the vertex (3, -8) and symmetry with respect to the line y = -8, we infer that the parabola opens upward or downward. The additional point (5, -4) that lies on the parabola helps us determine the specific equation of the parabola. Since the symmetry line is horizontal, the parabola will have an equation that follows the format y = a(x - h)² + k, where (h, k) is the vertex. Using the point (5, -4), we can substitute these values into the equation to solve for the coefficient a, which dictates the parabola's width and direction of opening.