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

Question

5341 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-10-29T21:09:27

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

by factoring out $2$ $2$ ,

$\Rightarrow y = 2 \sqrt{2 (x + \frac{3}{2})} + 1$ $Rightarrow y=2sqrt{2(x+3/2)}+1$

by pulling $\sqrt{2}$ $sqrt{2}$ out,

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

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

enter image source here

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

enter image source here

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

enter image source here

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

enter image source here

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

I hope that this was helpful.

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