The graph of f(x), shown below has the same shape as the graph has the same shape as the graph of g(x)=x^4-x^2 which contains the (0,0) which of the following is the equation of f(x)

First of all it is always a good idea to graph a question like this one. Here are the three graphs 

y = x^4 - x^2                   Color: Red            This is the base graph
y = x^4 - x^2 -  4             Color Blue            This has - 4 added to it.
y = x^4 - x^2 + 4             Color Green          This has 4 added to the base graph

Which one is correct? The red and blue one are not. The graph you want is plotted  upward from the base graph. The base graph (red nothing added to it) is not right because it has points on the x axis. The graph you want does not.

The same is true of the blue graph. It cuts the x axis. That only leaves the green one.

C