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Welcome so I have a whole little playlist on how to convert from standard form to vertex form but I figured I'll just do one little video just so you have an idea in case you come across some problems where you have to being able to solve or graph you have to be able to convert from standard form to vertex form so I figured I'd make a nice little video for you to do this so what we're planning on doing is going from y equals ax squared plus BX plus C and converting that to y equals a times X minus H squared plus okay and you know there's a lot of reasons why we want to go through from skander form to vertex form a lot of times it's easier to graph it's very easy to find the vertex and so forth however it's not always so simple to convert from one to the other so what I did is I did I'm gonna do three examples for you now the main important thing when we look at standard form out of vertex form is we notice that vertex form has a binomial squared and when we take a binomial and we square it what we get is what we call a perfect square trinomial all right and that's what bike what we're going to do is we are going to create what we call a perfect square trinomial and we're gonna do that by what we call the process of completing the square so there's gonna be a couple steps and I'm just gonna kind of go through each one individually and I'm actually gonna do it for each problem all together now the first step though we need to do is we need to make sure that when we are creating a perfect square trinomial that we have a is equal to one so here you can see we have a equal to one so we're all set over here though I have a negative right that's a negative one so what I'm gonna have to do is factor that out now I'm completing the square I only like to factor out of the first two terms so I have y equals a negative one times x squared minus 6x plus 11 all right now I'll talk about again completing my perfect square and what we're going to do but as long as it my a now is equal to one I'm all set over here I have to factor out a 5 it's all factor out of five so I have y equals five times x squared plus two x plus one now again I'm only factoring out of these first two terms because I'm going to show you what I'm gonna do is I'm going to now create alright and what we're gonna do is we're gonna look at only my quadratic in my linear term so right now those are a by knowing what I'm going to do is I'm going to take those terms and creep make them into a perfect square trinomial and I'll show you how so to do that what we're gonna do is we're gonna take B divided by 2 and then square it so in this case might be if we add ax squared plus BX plus C B is my coefficient of my linear term Sesame 4 divided by 2 squared well 4 divided by 2 is 2 2 squared is equal to 4 here might be divided by 2 is going to be negative 6 divided by 2 squared well negative 6 divided by 2 is negative 3 negative 3 squared equals 9 here I'm gonna take 2 divided by 2 and then square it and that equals 1 so now what I'm going to do is that is my value that completes my perfect square so what I'm gonna do with each one of those values is I'm now going to add it to my other two terms and that what that's going to do is that's going to now create a perfect square trinomial so let's go ahead and write that out now so when I add that in there so I have x squared plus 4x plus 4 now what I've done is I have created a perfect square trinomial and then I'll just have minus 5 I'll come back and I'll explain something in a second so here I'm gonna add 9 now inside the parentheses so I'll have y equals negative x squared minus 6x plus 9 plus nine plus eleven and then over here I'll add one inside the parentheses so I have y equals five times x squared plus two x plus one plus one okay so notice how everything else is staying the same the only thing I did is I took my middle value divided by 2 squared it and then added it to my quadratic in my linear term to create a perfect square trinomial right okay now adding this number is great but you got to look at this and we have an equation going on when we have an equation you just can't add numbers to one side of the equation without adding them to the other side of the equation right if I have so if I have an equation if I add one to the left side I have to make sure I add one to the right side so that was a proper about using our properties of equality so right now you can see all to the right side I'm adding a value now when solving a lot of times what we like to do is we like to add it to the other side as well because that's going to be your equality however when I'm trying to convert it from one form to the next I'm still solving each value for y so rather