 2 is equal to x minus 3 whole square. I am not worried about the coordinate of the vertex. So, please mention the vertex coordinate is a graph that we got. Now, may I make you pass through origin, please check. Does origin satisfy it? Don't make it like pass through origin and all, unless until you are doubly sure it passes through 0 comma 0. In this case, it doesn't. One more thing you do, on the graph also show where it cuts the y-axis. On the graph, like this, showing x and y-axis. What is 0 comma 1? And also where it is cutting your y-axis. Go step by step. Where it cuts the y-axis? You just have to plot where it cuts the y-axis. Roots is where it cuts the x-axis. I am not worried about the roots right now. Guys, I am not worried about the roots of this quadratic. I am not asking you. There is a difference between. I am not asking you. I am just asking. Now, we say that this graph has evolved from the graph of y is equal to x square. That's why sometimes I call it as skeleton graph. So when I say, what is the skeleton graph for it? It starts from here. These changes that you see, that is, your x has now become x minus 3, y has now become y plus 2. This is something which we can take care of later on. But the skeleton, what we call Hindi as dhacha. Human body is a skeleton. And the way the other parts are packed, that makes the person different from the other. But all of us cut the same skeleton. So all these types of graphs come from a skeleton y equal to x square, which you know is like this. Yes or no? Now, go step by step. First, what do you want to do? First, you want to replace y with y plus 2 or you want to change x with x minus 3. Your call? Krishna, what's your call? Krishna says, let's do the transformation on x first. So he is transforming or he is replacing x with x minus 3. So according to Krishna, where should this graph go? 3 units to the right. 3 units to the right. So can I say the graph will now look like this and draw it in different colors so that it can relate to it. So this is the graph. Now, let me change the color once again. If I do y plus 2, that means I am replacing my y with y plus 2. So what will happen to this graph? Downward to or upward? See the rule. When you change y with y plus h, h being a positive quantity, graph will bump h in its down. So the same vertex point will now come 2 units down. So it will appear like this. So this green one is your final graph. Now this vertex position will be what? From 0, 0 you took it to 3, 0. From 3, 0 you are bringing 2 down. So what will this position be? 3 comma minus 2. And how to know where it cuts the y-axis? I am not asking you where it cuts the x-axis because for cutting the x-axis you need to solve that equation which I don't want you to do right now. I will talk about it in a separate chapter with you called quadratic equations. Even though you have done it in class 10, there is still another quadratic equation for you in 11th as well. So in order to know where it cuts, in order to know where it cuts the y-axis, what you put 0 is x. So the moment you put this as 0, you will come to know that your y value will be 7. So this point here that you see is actually 0 comma 7. Understood? Let's try to see whether we get this on GeoGebra. One of you may be having Facebook app and all of your phones right? Anybody is having a graphing tool on their phone? I used to. I used to. See, this shows your seriousness. So please download graphing software called jesmos. Yeah. All your calls. Yes. Yesmos. B-E-S-M-O-S. Okay. On computers, if you're using a laptop, there is a very GeoGebra. GeoGebra.org. Okay? For phone, you can use jesmos. If you're using a laptop or a PC, open to GeoGebra. On your system and cap, no need to operate it online. GeoGebra, if downloaded on phone, may be very heavy for you, for the phone. Use jesmos for the phone. GeoGebra for the laptop or PC area. Okay. So let's got jesmos. This is the logo. Okay. So when you open it, you'll see this kind of interface. You can plot, you can type in any function that you want and it'll plot it for you. Okay? But right now, I'm showing you on GeoGebra. In GeoGebra, you can see locus also. You can shift the position of the points. What are the questions which I gave you just now? Let's do it. A chapter takes place. Okay. So as you can see, this point is... If I change... If I change here... So X minus 3... Super. You see that the red one, now... If I change it to Y plus 2 is equal to X minus 3... Square. You see that it has now come down by 2 units. Now this is the new position of the... This is the new position of the vertex. A becomes the new position of the vertex on this graph. Now next function that I'll give you, I'll use the board also simultaneously. The function given to you will not be as... Did you just stop? In fact that's the question in your worksheet as well. Y is equal to X square minus 8X plus 3. Now how will you plot this? Factorize it. Factorize it. It is not factorizable and we don't need to do that. Think, think, how can you do this? So instead of directly telling you the change in... Do you want to say? Yes. Do you want to say something which is not covered yet? Yes. It's not required. So this question is, try to complete this square in this case. So this, if you see these two terms, most of you would have already done the exercise of completing the square in capital X. So X square minus 8X would be generated by squaring which linear expression? X minus 4 the whole square, isn't it? So X minus 4 the whole square, the moment you expand it you get X square minus 8X but additionally you get a plus 16. So I don't need that. So if I just looking at these two terms, I don't need that extra 16 term. That's why I subtracted it off. Then this P I add it over it. Is that fine? By doing so you would realize that it becomes like this which is nothing but Y plus 13 is equal to X minus 4 whole square. Now this tells you the complete story. This tells you that make of Y equal to X square graph, shift the graph 4 in it soon. Right? I mean you're right. So if I have to plot this graph, Y is equal to X square minus 8X. Because it is showing it to be a turning point, a turning point is actually your vertex. Understood? So can you relate it to what transformation I have got there? My Y has got replaced with Y plus 13. That's why the graph came 13 down. My X got replaced with X minus 4. That's why my graph came 4 units to the right. Is that understood? Yes.