hello everyone and welcome to this lesson so in this lesson we are going to see how to convert a standard parab equation into Turning Point form okay so that might not make a lot of sense right now but what I mean is the following if they give you an equation like this for example FX = x^2 - 4x - 6 then what they like to do in exams and this confuses students is they say write F ofx in the form form and then they say FX = a x - p^ 2 + Q so we going to need to know how do we convert from this equation to this over here and what we're going to do is we're going to use completing the square so let's see how we do this the first step is to always make sure that the number in front of the x² is a 1 which in this case it is okay so we're going to say FX isal to x^2 - 4x so you write the first two parts like that then you add this new piece which is going to be plus then you open up a bracket squared and the number that you're going to put in here is whatever this number is over two like that then we've just added something now you can't just add something you can't just change the sum so to correct that we're going to minus it I know it seems a bit weird that we just adding and minusing but this is how it works and then the original minus 6 will just go over there so let's compare carefully what we've actually done we've taken this original equation up here we've still got all the parts there they are but in the middle we've got this part over here so that is what we've added so we added half of this number and then we squared it and then we just minused the same thing now going into the next line we take these three parts over here and they're going to go into one bracket now the two numbers that have have a square so that thing over there and that thing over there they are going to go there and there people often ask me what happens to this minus 4 it seems that it's going to disappear but I promise you it is hiding in the background if you had to multiply everything together you would see it is there so we're going to say x and then please if this is - 42 feel free to simplify that so - 4 over2 is just -2 and then this part you want to just put that all on the calculator and that part is just going to give us -2 now look what we've done guys we have converted this equation over here into this over here and that is in the form a x - p^ 2 + Q where our a value is just a 1 our p is a two and then our Q value is min-2 now why would we want to do this well the most simple answer is obviously that you get marks for that it's something that teachers want you to know but what is its main feature well the main main feature is is that this over here will end up being the turning point of the parabula so we can say that the turning point of the parabula and remember always take so if this is a minus 2 then that means the turning point is actually positive2 and then this over here will be your y value of your turning point and that is why this type of formula over here is very useful because it gives us the Turning Point straight away let's practice another one so what we do is we're going to convert it into that form again so we write down the first part and then we can also put the minus 8 at the end Okay so we've got everything the same then in the middle over here we're going to do a few things we're going to add whatever this number is over two so it's going to be like that then you square it but then you also minus the same thing so it's - 5/ 2^ 2 and that's it now what we do is these three parts over here they're going to go into to one bracket okay the two things with the square which is this one and that one over there so you're going to open up a bracket like that and it's going to be a x and a - 5/ 2 and then this last part here you just put on the calculator and that'll give us -4.25 and there we done so what this now tells us is that the turning point x value is 5/ 2 and the turning point Y value is -4.25 of course you could work out the turning point of this equation by using the turning point formula for x which is - b/ 2 a then once you turn you find the x value you could substitute that back into that equation to get the Y value but it would give you the same as what we have just found over here but please you must know how to do this step because you are going to get a couple of marks in the exams I've seen them ask this for four or five marks sometimes