 Hello, and welcome. We're going to do another screencast dealing with GeoGebra and some of its graphing capabilities. In this one we're going to be graphing equations and setting the viewing window for the graphs. This time we're going to show how to use the menus to set the viewing window, rather than using the graphical method of kind of stretching or contracting the axes and moving the graphs around. So here's what we're going to try to do here. We're going to start with graphing this equation, x squared plus y squared equals 1. And many of you may know, it's not necessary that you do here, but many of you know, I hope most of you, that graph of that is a circle. It has a center at the origin, at the point 0, 0, and has a radius of 1. Now if you're using your graphing calculator in its normal function mode, it is possible to graph that equation, but it takes a little bit of work. The first thing you have to do is solve this equation for y. That's because in function mode your calculator will only graph things of the form y equals f of x. And so what you will get here are two possible solutions for y. One of positive square root and the other the negative square root. And basically what you have to do is superimpose the graphs of those two equations. Now for this equation, it wasn't too difficult to solve for y. For other equations, that can be a very difficult thing and sometimes impossible thing to do. So it's nice to have the ability to be able to graph equations. So what we're going to do here is graph the equation of this circle and the graph of this second equation. And again, this one you may not be quite as familiar with, but some of you may recognize this as the graph of an ellipse. The center of this ellipse will be at the point 2, 0. And we will see that when we do get the graphs sketched. So here we go with geogibra. And again, we have our blank algebra view and our blank graphics view. And the nice thing here is we can simply go to the input line, input the equation, and geogibra will attempt to sketch the graph. And what you see there right now is something that really doesn't look like a circle. Remember, it's supposed to be a circle. And the main reason for that is if you look carefully, one unit on the y-axis is very different than one unit on the x-axis. So we can try to make adjustments by doing something like that and saying, okay, that looks pretty good. That looks like a circle. The other way is to be a little more precise with it and use the menus to do this. And the way we use the menus for viewing window in geogibra is we go to the options, go to advanced, and this is the graphics symbol. And you can see the pop-up there. It comes up preference, graphics. Click that. And now you see something much like your graphing calculator where you can enter x-min, x-max, y-min, and y-max. For getting the axes in the correct ratio, this next line is very nice. It basically says what ratio do you want the axes. To get this in true perspective, so a circle will look like a circle, we're going to want to change that to a one-to-one ratio. Before we do that, we might be interested in saying just change the x-axis since we know the radius is one. Let's just go from minus two to two and now come down here to the ratio and change this to one-to-one. And when I hit enter, I have to do notice what will happen with y-min and y-max. Those get changed. And what we can now do is look at that and say, okay, yet we've got our circle. We may want to move it. So we grab a hold of the move tool and move it into a position that we like. And again, with GeoGebra to superimpose any graph, we just, okay, tell it to graph the next thing. That'll be another equation. x minus two, that whole thing squared, divided by two, plus y squared equals one. And GeoGebra will attempt to graph that. And the whole thing doesn't quite show up. But you can kind of start seeing the elliptical shape there. We can try to move and it doesn't look like we're quite going to make it. Try to set the viewing window by the menu. Notice I'm going from minus one here and three or so is out a little further. So when I look at that, I might use that to kind of give me some advice on how to set the viewing window. If I don't get it right, we can always go back and change it. But just to save a little room, maybe we'll go from minus two to four. And hopefully that will encompass the whole thing. And again, we'll change the ratio to one to one, so our circle looks like a circle. And there we have it. Nice picture of those two graphs. And just this kind of one last little thing of review. If we wanted to find the points of intersection, yes, we could use algebra, but GeoGebra will also illustrate those points and give us decimal approximations for those coordinates. We go up to the point menu and select intersect two objects. And then simply select the two objects that we want to use. And now we get the two points A and B. I currently have GeoGebra set to four decimal places for rounding. If you want another rounding option again, just go up to options, rounding. Set it to two, three, four, whatever, so if we did three, now we've got a three decimal digit approximation of those coordinates. So actually, graphing equations in GeoGebra is quite easy. And I hope you find it to be a useful tool. Good luck with using GeoGebra and so long.