00:02
The given equation is in the standard form and we have to convert in the vertex form.
00:07
For that, we have to use the method of completing square.
00:10
Okay, so let's rewrite the equation here.
00:14
Now what we do, we have to take 2 as common from the entire expression.
00:19
As we take 2 common, we get x squared plus 4x now 2.
00:24
Basically, whenever we take 2 as common means we're going to divide this 2.
00:27
So as we divide 2 here in 3, we get 3 over 2.
00:31
After that, we need to use a kind of.
00:33
Identity that is a plus b whole squared is equal to a squared plus 2 a b plus b squared this is the first term okay let me just write the identity first it's square of a plus b which is the first and plus second term whole square is equal to square of the first term plus two times first term and the second term plus square of the second term so right now we already have the first term as a squared now what to do we have 4x here we have to convert it in the form of 2 a b so we can write 2 by default.
01:05
The first term is x itself.
01:07
And the second term we can write as 2 so that it's equivalent to 4x.
01:10
And that works because that's what we have in the middle.
01:13
But in the formula, we exactly have b squared here.
01:16
So we want to have 2 squared here right like this.
01:19
We can add it.
01:20
And immediately we subtract that because we did it from our end.
01:23
Still, it's equivalent to 0.
01:25
It means we haven't done anything wrong.
01:27
Also 3 over 2 is there.
01:28
We have to keep it like this.
01:30
The advantage of writing it in this way now, we have completed a square or completed an identity which is a squared plus 2ab plus b squared that can be rewrite written as a plus b whole squared so it's a plus b whole squared and rest of the terms we can write as it is 3 over 2 is 1 .5 let's now simplify this let's come to the next page here i can rewrite the equation so that's what is our expression but it's still not complete because 2 is outside in the bracket and that has to be multiplied using the rest of 2 22 property so what to do we finally get this expression 2 times x plus 2 whole squared negative 2 .5 times 2 is 5 so this is our vertex form right now now we compare it with the given form so that we can get the vertex value for vertex so it's h comma k h comma k is a vertex in that form so h is basically negative h is compared with positive 3 so we get h as negative 2, whereas k is negative 5.
02:35
So this is a vertex.
02:37
That's how we got the vertex.
02:38
So these are the two answers.
02:39
The first answer is this one, the first one where they asked you to write in this specified form.
02:45
So this is what we have right now.
02:47
This is the first answer.
02:49
And after that, they asked you the vertex.
02:51
So this is the second answer after that.
02:54
Let's see here what they asked.
02:55
Yeah.
02:57
So the first one we did, even the second one we did in the a part.
03:00
Now the b part, we have to graph it.
03:03
So we already have figured out the vertex of this parabola...