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

1 Answer
Oct 29, 2014

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.