00:01
Given quite direct equation is y is equal to 2x squared plus 12x plus 13.
00:07
And i'm going to put this into vertex form.
00:10
So in the form, y is equal to a times x minus h quantity squared plus k.
00:18
Okay.
00:19
And the vertex is just at the point h comma k.
00:22
So to do so, well, we take our equation here in standard form.
00:27
We can basically have this basically consider it set equal to zero, and then we want the constant by itself.
00:34
So on the other side of the equation.
00:36
So we have 2x squared plus 12x, and then move the 13 over, so this is equal to negative 13.
00:46
Now, to complete the square, we need to have the coefficient on our quadratic term.
00:53
So the coefficient on the x square term needs to be 1.
00:57
So right now it's two.
00:59
So what we can do is we can go ahead, we can factor out a two.
01:03
So we factor a two and we get two times x squared plus six x, right? you can always check.
01:11
If we distribute, we get two x squared plus 12x.
01:14
So and then this is then equal to, well, negative 13.
01:17
Okay.
01:18
So now we can complete the square on what's in the parentheses here.
01:22
Once we have the coefficient on the x squared term being one, we can go ahead and complete the square.
01:28
So to do so, well, we have two times we just copy down x squared plus 6x.
01:35
Now what we do is we take half of the coefficient on our linear term.
01:40
So half of six is three and then we square it.
01:44
And then we add that.
01:45
So we take half of the coefficient six, three, and then we square it.
01:49
So three squared is nine...