Summary Quick Guide to Completing the Square (Youtube) youtu.be
1,111 words - YouTube video - View YouTube video
n/a Guys. In this video, I wanna give you a quick guide to completing the square. Now there's a lot of reasons that we want to complete the square. We can use that to write it in Vertex form to identify the vi... X of the p, and sometimes we can use completing the square to solve them.
n/a But in this example, what I wanna do is just kind of like give you the basic idea of what we're trying to achieve Dex when we are completing the square. And I think the main thing that I want you to understand is the idea of creating this perfect square. So let me just go ahead and change this out a little bit, And I think this is a rule that I want you to use anytime that you are struggling. 1 thing I always like to tell my students like, you know, when you're learning something and you're taking a test or anything else. And maybe the numbers kinda of seem trickier, You're not really sure what to do.
n/a Like, go back and use some basic numbers. Okay? So what I'm gonna do is I'm gonna actually change this equation over here to something that's a little bit easier for me to understand. Alright. Now you might be wondering why you pick these numbers, like, what's what special about this.
n/a Well, the reason special about this is this is what we call a Perfect square tri I remember, perfect square tri no are are going to be tri ones that your first term squared and your last term squared. And what's so important about a perfect square tri. And is that they can be factored down into a bin squared. So you can see, like, in this example here, this is exactly what I'm looking for this is going to be my vertex form. That's what I'm trying to create when I am completing the square.
n/a 1 thing that I, you know, I want you to kind of ideas is like, when you're looking at, you know, trying to complete square, I'm gonna kind go through this in 2 different methods on 2 different ways. 1 thing I want you to think about is like, alright. If I need to take this, and I need to create this bin no squared. Right? That's what is putting things into Vertex form.
n/a Like what number do I need? Well, obviously, I already have an x squared and A6X, Right? I just need that 9. I don't want the 8. I just need at 9.
n/a So 1 thing you could do is just say, well, alright. Well, why don't we just add the 9 then. Right? Right and let's just go ahead and add the 9... 0, my get and yellow here.
n/a And then, obviously, we know that well, you just can't, like, add a 9 to 1 side. Right? Remember we either you're gonna add 9 to 1 side. You have add 9 to the other side. Alright.
n/a And then remember, like, the other thing is like, don't forget about the 8. Like, the eight's still there. You just can't like, not forget about the 8. So let's just go ahead and write the 8 over here. Okay?
n/a Now here's something that's really important. Actually, let me write this in with there. Okay. So so Now what we did is we've knew, if we had an x square plus A6X, we knew the number that was gonna create that perfect square tri was a not. So I just added that 9 in there.
n/a Right? Kinda like some math magic. But it's okay because I added a 9 unto both sides. Right? I mean, again, if you have an equation, as long as you're doing 1 thing to 1 side, you're doing the same thing to those side, it's gonna be okay.
n/a You're still keeping an equivalent equation. So now I know that this factors down to this by no squared. So now I can have a Let's see an x plus 3 quantity squared. Now again, if I wanna solve for y. Right?
n/a What are you gonna do? Well, you're going to subtract a 9. On sides. And therefore, remember this let's go to there. So 8 minus 9 is going to be a months 1.
n/a And there you go. Now, there is a way to kind of work through a problem when you kind of know what you're working with as far as creating a perfect square our Tri. But let me go through this exact same process. If we didn't already recognize a perfect square tri. If we didn't know x square plus 6 x that is gonna give us 9.
n/a So let me just kinda do the exact same problem, but also give you some... Some different ways to kind of approach it. So 1 thing that you always wanna do is we have these first 2 terms. Again, that is what you're gonna wanna look into creating that perfect search. So we'll do is we'll put parenthesis around them.
n/a Then the next thing we wanna do is like this 1 was obvious, Right? I kind of like per like, I wanted you to recognize that relationship. But 1 of the hard things about completing the square. Is not always as obvious what the what the value is that creates the perfect square Try tri no. So what we can do to always find that value is take our b divided by 2, and square.
n/a So in this case you would have a 6 divided by 2, squared which is going to equal a 9. Now, rather than adding the 9 sides. Notice what I had to do. I subtract it, right? From both sides say sell for the y.
n/a So what I like to do is I like to add and subtract it on the same side. So I have y is equal 2AX squared plus A6X. Right? We're gonna do a plus 9. So And then what we're gonna do is a minus 9 and then plus 8.
n/a Right? Because isn't that exactly what happened anyways, Like I had to add the 9, then I had the subtract 9 anyways. So this is just a... This is just making this process go by much quicker. And now I have created my perfect square tri, so I can go ahead and factor it down.
n/a So that is a quick easy way to complete the square. But if you wanna know a step by step method for completing the square, then that's gonna come up in the next video.