How do you graph Y=(x+3)^2?

It's just $y = {x}^{2}$ moved three times to the left
Any number thats subtracted or added in a parenthesis with $x$ changes the way the graph is
If you have $y = {\left(x + 3\right)}^{2}$ the graph is going to get moved three times to the left and if it's $y = {\left(x - 3\right)}^{2}$ the graph is going to get moved three times to the right.
As for graphing just pick a $x$ value like $3$ and plug it in
$y = {\left(\left(3\right) + 3\right)}^{2}$ or $y = 36$
You know the graph is going to start at (-3,0) as I explained above so just keep picking $x$ values to get a more accurate graph.