Answer:
[tex]f(x)=x^{2}+1[/tex]
Step-by-step explanation:
we have
[tex]g(x)=x^{2}[/tex]
This is the equation of a vertical parabola open upward
The vertex is a minimum
The vertex is the point (0,0)
The graph of f(x) has the same shape as the graph of g(x), but is shifted up 1 unit
so
The vertex of the function f(x) is (0,1)
The rule of the translation of g(x) to f(x) is
(x,y) ----> (x,y+1)
therefore
The equation of f(x) is equal to
[tex]f(x)=x^{2}+1[/tex]
