Final answer:
The question seems to inquire about function transformations, specifically g(x). However, the provided information is insufficient to accurately determine the transformation or provide a conclusive answer without additional context or details about the original function and transformation rules.
Step-by-step explanation:
The question is asking about the transformation of a function, specifically looking for the correct form of g(x) after a transformation is applied. It seems to involve concepts related to quadratic equations and possibly their transformations, but the provided information contains fragments that reference projectile motion equations and properties of parabolic functions, as well as the quadratic formula.
However, from the given context, it's challenging to address the transformation without a clearer definition of the original function or the specific transformation rules being applied. Transformation of functions in mathematics typically involves shifts, stretches, or reflections based on modifications to the function's formula.
To address this correctly, we would need a clearer question with more specific details concerning the initial function and the nature of the transformation applied to g(x).