g(x) = (1/4)x^2 . correct option C) .
<u>Step-by-step explanation:</u>
Here we have ,  and we need to find g(x) from the graph . Let's find out:
  and we need to find g(x) from the graph . Let's find out:
We have ,   . From the graph we can see that g(x) is passing through point (2,1 ) . Let's substitute this point in all of the four options !
   . From the graph we can see that g(x) is passing through point (2,1 ) . Let's substitute this point in all of the four options ! 
A . g(x) = (1/4x)^2
Putting (2,1) in equation  g(x) = (x/4)^2 , we get :
⇒ 
⇒ 
Hence , wrong equation ! 
B . g(x) = 4x^2
Putting (2,1) in equation g(x) = 4x^2 , we get :
⇒ 
⇒ 
Hence , wrong equation ! 
C . g(x) = (1/4)x^2
Putting (2,1) in equation g(x) = (1/4)x^2 , we get :
⇒ 
⇒ 
Hence , right equation ! 
D . g(x) = (1/2)x^2
Putting (2,1) in equation g(x) = (1/2)x^2 , we get :
⇒ 
⇒ 
Hence , wrong equation ! 
Therefore , g(x) = (1/4)x^2 . correct option C) .