Answer:
[tex]f(x)=x^2[/tex]
Step-by-step explanation:
All three functions in the figure are parabolic and thus share the parent function [tex]y=x^2[/tex]. They are horizontally dilated by some constant (unless they aren't) and can all be represented with [tex]y=\pm ax^2[/tex], where [tex]a[/tex] is some constant.
Plug in point the line passes through to find that constant. For [tex]f(x)[/tex], we can see the function clearly passes through (2,4):
[tex]4=a\cdot 2^2,\\4=4a,\\a=1[/tex]
Therefore, the function of [tex]f(x)[/tex] is [tex]f(x)=1x^2=\boxed{x^2}[/tex]
