Final answer:
The conic section represented by an axis of symmetry at x = -3, two points (-7, -2) and (-5, -8), and an upward opening direction, is likely a parabola.
Step-by-step explanation:
Given an axis of symmetry at x = -3, two points (-7, -2) and (-5, -8), and an upward opening direction, the type of conic section represented by this information is most likely a parabola. A parabola is the only conic section that has a single axis of symmetry and an opening direction. The information provided indicates that there is a symmetrical relationship about the vertical line x = -3, which is typical of a parabola. In addition, since parabolas can open upward or downward (but not side-to-side like ellipses or hyperbolas), the upward opening direction further suggests that the conic section is a parabola.