Final answer:
The standard form of the parabola with the vertex at the origin and focus at (0,7) is y = ¼(1/28)x², which opens upwards.
Step-by-step explanation:
The question asks for the standard form of a parabola with its vertex at the origin (0,0) and focus at (0,7). The standard form for such a parabola which opens upwards (since the focus has a positive y-coordinate) is y = ax². To determine the coefficient 'a', we use the relationship between the focus and the directrix. The distance from the vertex to the focus (focal length) is 7, so the directrix is at y = -7. The focal distance 'p' is thus 7, and since 'a' is 1/(4p), in this case, 'a' = ⅛(1/28). The standard form of the parabola is therefore y = ⅛(1/28)x².