Answer: Option C
[tex]f(x) = x^2;\ k (x) = x ^ 2 -7[/tex]
Step-by-step explanation:
Whenever we have a main function f(x) and we want to transform the graph of f(x) by moving it vertically then we apply the transformation:
[tex]k (x) = f (x) + b[/tex]
If [tex]b> 0[/tex] then the graph of k(x) will be the graph of f(x) displaced vertically b units down.
If [tex]b> 0[/tex] then the graph of k(x) will be the graph of f(x) displaced vertically b units upwards.
In this case we have
[tex]f (x) = x ^ 2[/tex]
We know that this function has its vertex in point (0,0).
Then, to move its vertex 7 units down we apply the transformation:
[tex]k (x) = f (x) - 7\\\\k (x) = x ^ 2 -7[/tex].
Then the function k(x) that will have its vertex 7 units below f(x) is
[tex]k (x) = x ^ 2 -7[/tex]
