Step 1 :The function \(f(x)=-\frac{1}{7} x^{2}\) is a transformation of the function \(g(x)=x^{2}\).
Step 2 :The negative sign in front of the fraction indicates a reflection across the x-axis.
Step 3 :The fraction \(\frac{1}{7}\) indicates a vertical shrink by a factor of \(\frac{1}{7}\).
Step 4 :There is no addition or subtraction inside or outside the function, so there are no horizontal or vertical translations.
Step 5 :There is also no multiplication or division by a constant inside the function, so there is no horizontal stretch or shrink.
Step 6 :Therefore, the transformations that need to be applied to \(g(x)=x^{2}\) to obtain the graph of \(f(x)=-\frac{1}{7} x^{2}\) are a reflection across the x-axis and a vertical shrink by a factor of \(\frac{1}{7}\).
Step 7 :\(\boxed{\text{A, D}}\)