00:01
Okay, we have a polynomial graph here, and we want to write the formula for the polynomial function of least degree.
00:10
All right, so let's talk about the least degree first.
00:13
There's kind of two ways we can go about that.
00:16
One is i have two different turning points.
00:19
All right, so two turning points means i have to have at least a degree three.
00:29
All right.
00:29
The other way i can think about it is i have one, two, three.
00:35
X intercepts, so three x intercepts, all right, which would also indicate for least degree that it would be three.
00:45
Now, let's go ahead and write our polynomial function.
00:49
So we're going to focus on those x intercepts first.
00:52
So i have an x intercept of negative 2, so x equals negative 2.
00:56
I have x is equal to 1, and i also have x is equal to 3.
01:04
Now, if i write these in factored form, i would have x plus 2, times x minus 1 times x minus 3.
01:12
And what i want to do is i want to multiply these factored forms together.
01:17
Let's do our first two.
01:19
I would end up with x squared minus x plus 2x minus 2, which simplifies to x squared plus x minus 2.
01:33
But i'm not quite done with the problem yet.
01:35
I still want to multiply by the last one.
01:40
The x minus three...