00:01
So number 14 says determine the equations with the least degree for each polynomial function and sketch the graph of each.
00:10
So i'm going to go through these and we can sketch the graph from there.
00:14
The first one is a cubic function with zeros at, with zeros at negative 3.
00:31
I'm just going to say the multiplicity is 2.
00:36
And two, and the multiplicity there is.
00:40
So that tells me what my three, what my two brackets are, but three of the brackets.
00:46
I'm going to have x plus three, because that gives me a zero of negative three.
00:51
I'm going to square it because of the multiplicity two.
00:54
And then i go with x minus two.
00:59
Now at the cubic, we've got a degree of three, so we have the correct equation for this.
01:07
The last thing that's mentioned here is the y intercept is equal to negative 18.
01:17
And to get the constant, we need to do some multiplying of the final terms of both brackets.
01:23
So i have three, but it's to the power of two because these brackets are twice.
01:28
So three times three times negative two.
01:32
And that is nine times negative two, which gives me negative 18.
01:38
So my y intercept is met by this equation.
01:44
So my final equation is.
01:46
Okay, so we know we have zeros at negative 3 and positive 2.
01:54
So let's get the points here.
02:00
And positive 2.
02:06
Okay.
02:07
And so my y intercept is negative 18.
02:10
So we need to get those points together.
02:14
And so negative 4, negative 8.
02:18
Negative 12, negative 16, and negative 20.
02:25
So there's my intercept there.
02:27
I have got my x intersets.
02:29
And so i know between negative 3 and positive 2, it's negative.
02:34
Because negative 3 has a multiplicity of 2, and we know that we are going to be in the negative side of the x -axis between 3 and 2, we know that the graph starts here.
02:47
And it comes down to here...