 Now let's look at how to find that maximum or a minimum on a graph. First we need an equation. So let's come over here to y equal and let's say Let's do 2x squared. So 2x and then curate 2 plus 3x minus 4 Totally random All right, so we want a standard window. So let's do a zoom six so we can see the graph And that's a great graph. We can see everything we need to do So if you look at this graph, it has a lowest point and the lowest point would be a minimum point on the graph To find a minimum we need to do second trace And then if you look up here at three that says minimum so we can hit our three And then you'll see it says left bound that means that I need to be on the left hand side of that lowest point So I arrow over to the left just get off of the vertex or the bottom Of that graph and then anywhere over there is fine If you're doing this with me and your numbers don't look quite like mine as long as you're to the left of that Vertex the lowest point then you can just press enter And then we'll say right bound which means we need to go through the vertex back to the other side And anywhere over there again, if your numbers don't match mine, it's fine. Just press enter And then for guess we always just press enter And we can now see that the minimum of that point is negative point seven four nine nine to we'll say negative point seven five and negative five point one two five Now what if we had at maximum Well, if we come back in here to y equal and we Clear out our equation and this time let's put in we need a negative and let's say negative X squared let's just do x squared this time negative x squared Remember the other way to do x squared is if you come hit this x squared key It'll actually give you the exponent of two So we'll show you both ways in this example It's negative x squared minus 10 x Plus eight And then we'll hit our graph. We should still be in a standard window And we can see the graph we can see the highest point or the maximum The vertex is a maximum in this case So we do the same thing we do second trace We went maximum this time so it's four And we're going to do the same thing left bound go to the left so arrow to the left So you're somewhere over there press enter Right bound so arrow back through the vertex into the right hand side anywhere and say press enter And press enter through the guess And we find out that that maximum is to look at that very closely We see that this is 6.6976, but then it's e to the negative seven That means that it is a there's six zeroes in front of that So it's very close to zero. We would round it to zero and negative two Let's try one more just to see if we can find a nice one So go back to y equal So we want negative x squared and i'm going to use the x square key down here This time to put the exponent of two on there And then we're going to say minus five x And then plus six And now we're going to look at our graph if we hit graph it should still be a standard window We can't quite see our vertex, which is a maximum so we need to go back into window It's a y that's a big y that's not quite big enough so we can just arrow down there to y max Instead of being 10 it was pretty close so we probably could go to 20 and be all right So press enter And then everything else should be fine so we can go back and look at our graph And now we can see the vertex in here And we can do second trace Maximum which is four And do the same thing go to the left hand side of my graph of my Vertex, so I got to keep going over here Anywhere over there as long as it's not on the vertex press enter Right bound we need to go back through the vertex and to the right hand side press enter Press enter for a guess And we see that it's the maximum where the vertex would be negative 2.5 and 12.25