Answer: Last option.
Step-by-step explanation:
The complete question is: "What is the equation of the translated function, [tex]g(x)[/tex] if [tex]f(x) = x^2[/tex]?
The missing graph is attached.
Below are shown some transformations for a function [tex]f(x)[/tex] :
1. If [tex]f(x)+k[/tex] the function is translated "k" units up.
2. If [tex]f(x)-k[/tex] the function is translated "k" units down.
3. If [tex]f(x+k)[/tex] the function is translated "k" units to the left.
4. If [tex]f(x-k)[/tex] the function is translated "k" units to the right.
In this case, you can observe in the graph that the vertex of the parabola (function [tex]f(x)[/tex]) is at the following point:
[tex](0,0)[/tex]
And the vertex of the translated parabola (function [tex]g(x)[/tex]) is at this point:
[tex](5,2)[/tex]
Therefore, based on the transformations explained before, you can identify that the function [tex]g(x)[/tex] is obtained by translating the function [tex]f(x)[/tex] 5 units to the right and 2 units up.
Then, the equation of the function [tex]g(x)[/tex] is:
[tex]g(x)=(x-5)^2+2[/tex]
