Answer:
Option C. [tex]g(x)=(x+3)^2+1[/tex]
Step-by-step explanation:
The complete question in the attached figure
we know that
The equation of the function f(x) is
[tex]f(x)=x^2[/tex]
Is a parabola open upward
The vertex is the point (0,0)
The function g(x) have the same shape
The vertex of the function g(x) is the point (-3,1)
so
The rule of the transformation of f(x) to g(x) is
(0,0) -----> (-3,1)
(x,y) -----> (x-3,y+1)
That means----> The translation is 3 units at left and 1 unit up
therefore
The equation of the function g(x) in vertex form is equal to
[tex]g(x)=(x+3)^2+1[/tex]
