A playground is enclosed and subdivided by 1700 feet of fencing, as shown in the figure to the right. Use a graphing utility to graph A of X equal X divided by or X * 1700 -, 2 X all divided by three, which expresses the area of the playground A in terms of one of its dimensions X. I'm actually going to show that how to do this without a calculator. So the first thing is to realize that two X + 3 Y equals the 1700. So I'm going to solve for Y, subtract my 2X divided by three and I see that y = 1700 - 2 X divided by three. So to find the area, the area is just going to be X * y or X * 1700 -, 2 X over three. If I distribute this out, I realize that this is just a graph of a parabola that's going to be going opening downwards, hence it'll have a maximum point. If I look at the X intercepts, the X intercepts come from setting the numerator equal to 0. So if you thought about setting the numerator equal to 0, we have the X times the 1700 -, 2 X all divided by three. Well if we just set the numerator equal to 0, we can see that X = 0 and X = 1700 / 2 which is 8:50. So the X intercepts are 00 and 8:50 zero. The vertex has to be exactly in the middle because of symmetry. So if I thought about taking the 2X intercepts and adding them together and dividing by two, that would be my axis of symmetry. So from the axis of symmetry, once I get this X value, I can just stick it into the function. Actually, I guess this should have said A because we're using A's, but we can stick it into the function to find the Y. So my X value or my vertex is 425 and my area or my output is 361,250 all over three. So if we know that X is 425, we can find our Y simply by substituting 1700 - 2 * 425 all over three. That's about 283 rounding. And then to find the area we can just go X * 17 - 2 X over three. It should also be the Y value of our vertex and it is so 120,417 feet squared for the area.