Answer:
The value of k is:
k=6
Step-by-step explanation:
We are given a graph of the function f(x) and g(x) such that both the graphs are parabola and the graph of g(x) is a shift of graph of f(x) some units to the left.
The vertex of the graph of f(x) is at x=4
whereas the vertex of the graph of the function g(x) is at x= -2.
This means that the graph of g(x) is a shift of the graph of f(x) 6 units to the left.
This means that:
g(x)=f(x+6)
( Since the translation of a function f(x) k units either to the left or to the right is denoted by:
f(x+k)
when k>0 the shift is to the left and if k<0 the shift is to the right.)
This means that the value of k is 6
