# How do you graph y=sqrt(2x) and how does it compare to the parent function?

Sep 2, 2017

$y$ is the standard graph of $\sqrt{x}$ scaled by $\sqrt{2}$

#### Explanation:

$y = \sqrt{2 x}$

Remember: $\sqrt{a b} = \sqrt{a} \times \sqrt{b}$

$\therefore y = \sqrt{2} \times \sqrt{x}$

Hence, $y$ is the standard graph of $\sqrt{x}$ scaled by $\sqrt{2}$

This can be seen below by the graphs of $y$ (upper) and $\sqrt{x}$.

graph{(y-sqrt(2x))(y-sqrtx)=0 [-2.38, 4.548, -0.54, 2.923]}