Answer:
To get the function g, shift f up by 3 units and to the right by 9 units.
Step-by-step explanation:
The given functions are
[tex]f(x)=x^2[/tex]
[tex]g(x)=(x-9)^2+3[/tex]
If f(x) is a parent function, then g(x) can be written in the form of f(x) as
[tex]g(x)=f(x-9)+3[/tex] ...(1)
The translation is defined as
[tex]g(x)=f(x+a)2+b[/tex] ... (2)
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.
On comparing (1) and (2), we get
[tex]a=-9,b=3[/tex]
It means, to get the function g, shift f up by 3 units and to the right by 9 units.
