Question

Which graph represent the function f(x)=4x^2

Answer 1

The graph of the function $f(x)=4x^2$ is a transformation of the graph of the parent function $f(x)=x^2$; more precisely, the graph of the function $f(x)=4x^2$ is the graph of the function $f(x)=x^2$ compressed by a factor of 4 in the $x$ direction.

Remember that we can compress or stretch the graph of a function in the $x$ direction by multiplying $x$ by a constant $c$.
if $c\ \textgreater \ 1$, we are compressing  the graph in the $x$ direction.
if $0\ \textless \ c\ \textless \ 1$, we are stretching the graph in the $x$ direction.

We can conclude that the graph of the function $f(x)=4x^2$ is the graph in the first picture. Also, in the second picture you will see the graph of both the function and its parent function simultaneously.