Answer:
The correct option is A.
Step-by-step explanation:
The parent quadratic function is,
\(f(x)=x^2\)
The transformation is defined as
\(g(x)=(x+a)^2+b\) ....(1)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0,then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0,then the graph shifts b units down.
It is given that f(x) shifted four units right and seven units down. It means a=-4 and b=-7.
Substitute a=-4 and b=-7 in equation (1).
\(g(x)=(x-4)^2-7\)
The required function is \(g(x)=(x-4)^2-7\).
Therefore the correct option is A.
