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

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Answer 1 · 2014-10-29T21:09:27

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

by factoring out $2$ ,

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

by pulling $sqrt{2}$ out,

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

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

enter image source here

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

enter image source here

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

enter image source here

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

enter image source here

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

I hope that this was helpful.

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