 Greetings. In this screencast, we're going to learn some of the basic graphing capabilities of the software package GeoGebra. For this screencast, our objectives are going to be to learn about the Algebra view and the Graphics view in GeoGebra, to learn how to enter a function in GeoGebra, to learn how to set the viewing in GeoGebra, and hopefully with your experience with a graphing calculator, you know that that can be a difficult task, but a very important task in trying to get an appropriate view for the graph of a function. We're going to learn how to use GeoGebra to approximate points of intersection of two graphs, and finally, we're going to learn how to plot some points in GeoGebra. So, here are the functions that we're going to be using. And so again, you might want to write these down, pause and write these down, so you have these at your disposal. And entering the function in GeoGebra just like in your graphing calculator, with this first function f of x with minus one half times x squared. When I enter that in GeoGebra, I'm going to use minus x squared divided by two. So that's going to be our basic setup. So here is the standard screen that you will see when you open up the GeoGebra program. And again, you have the algebra view over here in the graphics view over here. And the other important aspect of it is going to be the input line down at the bottom here. That's where we're going to be entering the functions that we graph. And for adjusting the viewing window and so forth, there are going to be two ways to do that. One will be similar to how you do that with your graphing calculator. And the other, we're primarily going to be using this button up here, which says move graphics view. And we'll show how to use that. It gives a very visual way to set the viewing window. So we're going to enter our first function. And you basically type that just like you do in the graphing calculator on a single line, except we can enter f of x equals, and now we can write minus x squared divided by two, minus 5x plus 7, and hit enter. And we will get our first view of a graph of that function. And as you can see, it's not a very adequate graph. It does not show much of the function and especially does not show the interesting parts of that. But one of the nice things you can do here is you can use this button, click on it, and you can move the graph around as you see fit. Eventually, you'll see, okay, we look up way up there and there seem to be a vertex. This is the graph of a parabola. And we might want to still show the axes. We don't want to just see the vertex, but we might want to see the axes as well. So I might start off with something, oh, let's keep the axes about right there. And when I'm in this move graphics view, one nice thing is if you go to the axes, notice what happens there, you get that double arrow. And what you can do is move the axes that way. And you might say, okay, for the x-axis, that seems fairly reasonable. It's showing the two x-intercepts. And what we have to do then is adjust the y-axis. And we do that by grabbing a hold of that, get that double arrow. And in this case, bringing it down. And, lo and behold, we now have a reasonably nice picture of the graph of that parabola. And that is a very nice way to set up the viewing window and adjust the viewing window, I should say, for a graph of a function in GeoGebra. If you want to use something more similar to your graphing calculator, it's kind of in a menu which isn't the easiest to find. I wish it would be a little easier, but it still is there. You go to options, advanced. And this little icon up here, you can see what pops up there is preference for graphics. And now you can see you have x-min, x-max, y-min, y-max. You can set those just like you do with the graphing calculator. We'll talk about this ratio down here, x-axis to y-axis in a future screencast. But right now you can see it's in a ratio of 1 to about 2.7. But I'm not going to adjust the viewing window any further than this right now, since we do have a nice viewing window for this particular function. And now we're going to enter the second function. And as I said, that one comes out, or we had set up as g of x equals a fairly simple one, a linear function, x plus 2. And when I hit that, I immediately get that. And you can see, again, this may not be the most optimal viewing window for this. When we add this new function, we might have to readjust the viewing window. In particular, it looks like we might want to readjust the y-axis. So again, I'll go up here and get that move thing and adjust there. I probably just want to move it up a little bit then. You can see how nicely you can kind of move this around. And now I have both points of intersection showing on the graph. And I can consider this to be a very nice graph of these two functions. It's also very easy to find points of intersection, or I should really say in this case approximate points of intersection. One way to do that, or probably the easiest way to do that, and that's just getting used to where some of these things are located, is this point menu up here. It says new point, but if you hit this little arrow, down arrow here, you get some other options, and in particular, intersect two objects. And when I intersect two objects, what I have to do now is select those. And you can see as I move to the graph of the parabola, it kind of becomes highlighted and I select that one. And then I go down to the straight line and it should highlight and select that one. And hey, there are my two points of intersection showing. And again, what's happening is in this graphics view, we see the two points of intersection in the algebra view. You can see the coordinates of those two points of intersection. Technically, those are the approximate coordinates. And the default for GeoGebra is to show two decimal places. If you would like to show more decimal places than that, again, you can go to options and a rounding option. And just select what you want, for example, four decimal places. And now I have the points of intersection correct to four decimal places. And that's kind of some basic graphing in GeoGebra. One last thing that I actually forgot to mention in the objectives, but is a very nice feature of this, is to, if you go to the file menu and export, you can copy the graphics view to clipboard. And that copies it to the clipboard. And what that allows me to do at this point is to paste that into a word processing document. And again, we will try to look at that in another screencast. Again, if you look at that export, you can actually save the graphics view in various formats. And again, that is something we will not look at here. So there you have the basic graphing capabilities of GeoGebra. And hopefully you can see it's relatively easy, but you might have to get some practice at doing it and play with it a little bit yourself. That's it for now. Thanks for watching.