Answer:
It means the graph of f(x) stretch vertically by factor 4, and translate 2 units right and 1 units down to get the graph of g(x).
Step-by-step explanation:
The parent function is
[tex]f(x)=x^2[/tex]
The given function is
[tex]g(x)=4(x-2)^2-1[/tex] .... (1)
The translation is defined as
[tex]g(x)=kf(x+a)^2+b[/tex] .... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
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.
On comparing (1) and (2) we get
[tex]k=4,h=-2,k=-1[/tex]
It means the graph of f(x) stretch vertically by factor 4, and translate 2 units right and 1 units down to get the graph of g(x).
