# How do you graph y = 2\sqrt{2x+3}+1?

Oct 29, 2014

$y = 2 \sqrt{2 x + 3} + 1$

by factoring out $2$,

$R i g h t a r r o w y = 2 \sqrt{2 \left(x + \frac{3}{2}\right)} + 1$

by pulling $\sqrt{2}$ out,

$R i g h t a r r o w y = 2 \sqrt{2} \sqrt{x + \frac{3}{2}} + 1$

Now, let us sketch $y = \sqrt{x}$, which looks like:

By stretching vertically by a factor of $2 \sqrt{2}$, we have $y = 2 \sqrt{2} \sqrt{x}$, which looks like:

By shifting left by $\frac{3}{2}$, we have $y = 2 \sqrt{2} \sqrt{x + \frac{3}{2}}$, which looks like:

By shifting up by 1 unit, we have $y = 2 \sqrt{2} \sqrt{x + \frac{3}{2}} + 1$, which looks like:

Above is the graph of $y = 2 \sqrt{2 x + 3} + 1$.

I hope that this was helpful.