The equation of the graph in red is given by
[tex]f(x)=x^2[/tex]
Let us find the equation of the graph in blue.
Notice that the blue graph is horizontally translated to the right by 3 units.
The rule for horizontal translation to the right is given by
[tex]g(x)=(x-d)^2[/tex]
For the given case, the translation is 3 units so the equation becomes
[tex]g(x)=(x-3)^2[/tex]
Also, notice that the blue graph is vertically translated upward by 1 unit.
The rule for vertical translation upward is given by
[tex]g(x)=x^2+c[/tex]
For the given case, the translation is 1 unit so the equation becomes
[tex]g(x)=x^2+1[/tex]
Finally, combining both of the translations, the equation of the blue graph becomes
[tex]g(x)=(x-3)^2+1[/tex]
