Question

How do the graph of y=√4x and y=2√x compare?

Answer 1

y=√x to y=√4x is a horizontal compression by a factor of 1/4.
y=√x to y=2√x is a vertical expansion by a factor of 2.

How are these two graphs equal?

Answer 2

go and download geogebra... a free graphing geometry package...

they are one in the same line

\[y = \sqrt{4 \times x} = \sqrt{4}\times \sqrt{x} = 2\sqrt{x}\]

just show the congruency via the algebra

But I have attached a copy of the graphs