Question 477556
First of all, you will certainly agree that a square has 4 sides, and that all 4 sides are equal in length. Also, if you are not already aware, the area of a square is all the space bounded by those 4 sides. The formula for the area is length times width, where the length is the size of a vertical side, while the width is the size of a horizontal side. However, since all sides are equal, the area is equal to the size of any side times itself(length squared, or width squared)

So, now we are given that some square has area x^2 +6x+9. What ever the length of a side is, when you multiply it by itself we should get x^2 +6x+9.

? * ? = x^2 +6x+9.

Now, directly taking the square root of a polynomial (such as x^2 +6x+9), is not necessarily obvious, or easy. So let's try to guess as wisely as we can.

(  )*(  ) = x^2 +6x+9
We need to fill the brackets and we have our answer, and note, whatever we do to one bracket, we must do to the other, since a square as equal sides, meaning the length and width have to be the same 'quantity.'

Let's start with x in the first bracket, immediately we get x in the second one, since we have to do the same to each bracket.

(x )*(x ) = x^2 +6x+9. We choose x, since x*x=x^2, so at least we get our first term. Now we notice the last term is 9, and that 9 is 3^2., so let's put a +3 in each bracket since 3*3=9. Doing this guarantees our last term, but there's going to be a middle term, let's hope it turns out to be 6x!
now we want to check what (x+3)*(x+3) actually expands into. If you are not familiar with these expansions, here's a general example that should explain it well enough to understand and solve this problem. If we have some (a+b)*(c+d), where a,b,c,d can be variables, or numbers, or anything really, then the expansion of (a+b)*(c+d) = (a*c)+(a*d)+(b*c)+(b*d); I believe this is known as the foil method.

Back to our problem, (x+3)*(x+3)=x^2+3x+3x+9 according to the formula. The two middle terms 3x, 3x can be added up since they are 'like' terms. 3x+3x = 6. 

Therefore, (x+3)*(x+3) = x^2 +6x+9 meaning the length of side is x+3 units.

For the graph, along the x axis (y=0), plot some point and label that point (x,0). Then, from that labeled points, move 3 "units"(which can be cm, or whatever scale you are using), to the right and plot that point as (x+3,0). Then from the (x,0) point move 3 units up, and label that (x,3). Finally plot and label a point at (x+3,3)(I'll leave it to you to figure out how to find where this last point is on the graph). Once you have the 4 points, connect them, and that's a graph of the square.