00:01
Let's write the following in vertex form, and then we can answer the following questions.
00:06
So let's start by looking what vertex form looks like.
00:09
That would be c of x equals a, x minus h squared plus k.
00:16
That means we need to complete the square on my x's.
00:19
So i'm going to do that here.
00:21
To do that, i'm first going to factor out that three, and that'll leave me with x squared minus 6x.
00:27
And then i'm going to have the plus 23.
00:31
So now i need to figure out what goes here to complete that square.
00:36
And to do so, we take half of negative 6, which is negative 3, and we square that to get positive 9.
00:43
Now, what that does is gives us a 9 here that we have to compensate for, but it's not just 9.
00:51
I'm going to be distributing that 3 to the 9 to get a positive 27.
00:55
Therefore, i compensate for that by putting a negative 27.
00:59
So i'm going to have 3x minus 3 squared minus 4.
01:05
There we have it in our vertex form.
01:08
So now it wants to know what is the vertex.
01:10
Our vertex is h and k.
01:13
So that means our vertex is going to be 3, negative 4.
01:18
Next, i want to know what wants to know what are the x intercepts.
01:22
Now the x intercepts are when our 1.
01:25
Value equals to 0.
01:28
So we're going to set this equal to 0, and i'm going to do it in the vertex form.
01:33
So 0 equals 3, x minus 3 squared minus 4.
01:39
I'm going to add 4 to both sides, divide by 3.
01:45
That means we're going to have 4 thirds equals x minus 3 squared.
01:52
Let's square root both sides.
01:54
So we're going to get 3.
01:55
Square root of 4 over 3, so that's going to be 2 over the square root of 3, equals x minus 3.
02:03
Now, and don't forget to put your plus or minus.
02:06
Now, i'll add 3 to both sides, and i'll have x equals 3 plus or minus 2 over the square root of 3.
02:15
Those are my x intercepts.
02:18
The y intercepts are really quite easier...