Answer: The correct option is (A) a shift down 1 unit.
Step-by-step explanation: The given functions are:
\(f(x)=x^2,\\\\p(x)=-50+14x-x^2.\)
we are given to select the correct option which gives one of the transformations applied to the graph of f(x) to produce the graph of g(x).
We have
\(p(x)=-50+14x-x^2\\\\\Rightarrow p(x)=-(x^2-14x+49)-1\\\\\Rightarrow p(x)=-(x-7)^2-1\\\\\Rightarrow p(x)+1=-(x-7)^2.\)
Comparing the equation of p(x) with that of f(x), we conclude that the transformations are
(i) a horizontal shift of 7 units to the right,
(ii) a vertical shift of 1 unit downwards.
So, one of the correct transformations is - a shift down by 1 unit.
The graphs of f(x) and p(x) are attached below.
Thus, (A) is the correct option.
