1
00:00:00;00 --> 00:00:03;00
Confirmed by these two factors. Ryan?

2
00:00:04;00 --> 00:00:07;14
How do you examine what me make that negative 1?

3
00:00:07;15 --> 00:00:08;06
Uh-huh

4
00:00:08;07 --> 00:00:14;14
Didn't you have to have a positive? Instead of a positive negative, a negative
positive?

5
00:00:14;15 --> 00:00:18;03
So how do you want me to change Gromick's hypothesis?

6
00:00:18;04 --> 00:00:20;10
No, just keep that one and make the other one positive.

7
00:00:20;11 --> 00:00:21;09
Oh. I'm sorry.

8
00:00:21;10 --> 00:00:23;05
Plus 4

9
00:00:23;06 --> 00:00:26;15
So, where would the zeros be for this function definition, Ryan?

10
00:00:28;05 --> 00:00:30;06
Positive 2 and negative 5

11
00:00:31;03 --> 00:00:33;10
So if I plug in positive 2, I'm going to get zero?

12
00:00:35;02 --> 00:00:39;01
Yeah, oh no

13
00:00:41;09 --> 00:00:53;10
Do you want to adjust anything? I think you're thinking about something correctly,
but you're, you just said, if I pick positive 2, you said that would make it zero.

14
00:00:53;11 --> 00:01:01;13
But what about 2 plus 2? Not zero. So we do want a zero at 2, but I don't think
this constant definition will give us that. Casey?

15
00:01:01;14 --> 00:01:06;10
There's no way any function will be able to make that graph

16
00:01:06;11 --> 00:01:07;08
Why not?

17
00:01:07;09 --> 00:01:21;06
Because like you said before, we used the negative factors, and two negatives
make a positive, but we're using positive factors to get a negative graph.

18
00:01:21;07 --> 00:01:25;03
It wouldn't work the same because it would still be a positive.

19
00:01:25;13 --> 00:01:30;02
OK, I think I see what you're saying, so first of all, what should these be guys?

20
00:01:30;03 --> 00:01:31;04
Negative 2

21
00:01:31;10 --> 00:01:43;01
We get minus 2 and X minus 2, what would the zero be? At positive 2. So this,
this I think is a better hypothesis.

22
00:01:43;02 --> 00:01:50;05
Casey's saying I don't think it's ever going to happen because Ms. Coombes, you just said that no matter what you plug in, a negative times a negative gets you

23
00:01:50;06 --> 00:01:51;04
A positive

24
00:01:51;05 --> 00:01:53;13
A positive. And a positive times a positive gets you

25
00:01:53;14 --> 00:01:54;09
A Positive

26
00:01:54;10 --> 00:02:01;14
A positive, and what I've drawn is negative values, agreed?
I'm in the negative Y values down here.

27
00:02:01;15 --> 00:02:12;01
But again, you can't forget about whatever else is on the outside. We just said that if
we plug in values negative times a negative gave us a positive on these factors

28
00:02:12;02 --> 00:02:22;10
As well, which kept the product positive. Could I have done anything, you think, that
even though I agree with you Casey, that whatever I plug in

29
00:02:22;11 --> 00:02:29;09
These two factors will always give me back a positive because of everything we
already talked about, but could I do something

30
00:02:29;10 --> 00:02:39;11
Maybe with what's going on over here that will allow my product to be negative. That will allow my product to be negative.

31
00:02:41;09 --> 00:02:50;01
You can change the sign of one of the other factors, like X plus 5 or X plus 7

32
00:02:51;02 --> 00:02:52;08
So I do something like that?

33
00:02:52;09 --> 00:02:52;14
Yeah

34
00:02:51;10 --> 00:03:07;11
OK, fine, we'll change that one. The green one that I drew goes through positive 5,
so we'll leave that one. I just let it stop there.

35
00:03:07;12 --> 00:03:19;07
How about this, let's ignore that one. Actually, what I've drawn, I have a zero at 2
and a zero at 5, but I actually didn't have it come back down. Let's talk about that.

36
00:03:19;08 --> 00:03:28;10
So, yeah, maybe what if one of these was positive, or what if one of them is not
even there? What if I only have X minus 2 times X minus 2, that would give me that.

37
00:03:28;11 --> 00:03:36;06
And then, times X minus 5, that would give me this. What do you think? Let's try it again.

38
00:03:36;07 --> 00:03:44;03
I plug in a positive 1. WIll the sign of the first graph be a positive or a negative
if I plug in 1?

39
00:03:44;04 --> 00:03:45;11
Negative

40
00:03:45;12 --> 00:03:47;06
If I plug in 1

41
00:03:47;07 --> 00:03:48;06
Negative

42
00:03:48;07 --> 00:03:50;00
If I plug in 1?

43
00:03:50;01 --> 00:03:50;12
Negative

44
00:03:50;13 --> 00:03:54;02
So, negative and negative?

45
00:03:54;03 --> 00:03:55;01
Positive

46
00:03:55;02 --> 00:03:57;08
TImes a negative?

47
00:03:57;09 --> 00:03:58;06
Negative

48
00:03:58;07 --> 00:04:04;06
Oh, what just happened? What's the overall product going to be?

49
00:04:04;07 --> 00:04:05;03
Negative

50
00:04:05;04 --> 00:04:11;10
Negative. What about in the neighborhood of these two factors? Positive. But then,
what does this side do to it?

51
00:04:11;11 --> 00:04:12;09
Negative

52
00:04:12;10 --> 00:04:21;07
Turns it back to negatives. So, that so far supports at least what's happening to the
left of the zero. Let's check to the right of the zero.

53
00:04:21;08 --> 00:04:25;14
We'll test a 3. If I plug in a 3 to the first factor. positive or negative?

54
00:04:25;15 --> 00:04:27;06
Positive

55
00:04:27;07 --> 00:04:30;01
3, so positive. Plug in a 3.

56
00:04:30;02 --> 00:04:31;00
Positive

57
00:04:31;01 --> 00:04:32;09
Positive. Plug in a 3.

58
00:04:32;10 --> 00:04:33;04
Negative

59
00:04:33;05 --> 00:04:36;00
Negative again, so positive and positive?

60
00:04:36;01 --> 00:04:37;02
Positive

61
00:04:37;03 --> 00:04:38;10
Times a negative?

62
00:04:38;11 --> 00:04:39;11
Negative

63
00:04:41;08 --> 00:04:52;08
Is that what I drew? Mmm hmm. So, that's exactly what I wanted to bring up,
because this one was almost too easy to say well of course it's going to be positive.

64
00:04:52;09 --> 00:04:59;12
Positive times a positive makes a positive. Negative times a negative makes a
positive. But, OK, that's true

65
00:04:59;13 --> 00:05:08;13
All that's really telling you is whatever happened to the left is going to happen again to the right. Because in the neighborhood of that zero

66
00:05:08;14 --> 00:05:15;03
It's acting the same way either to the left or the right, it doesn't matter.
So, whatever happens to the left will happen again if you go to the right.

67
00:05:15;04 --> 00:05:24;07
Because of what we talked about. But, you can't ignore what else is going on.
Whatever else, whatever factors are being multiplied, they've got signs too.

68
00:05:24;08 --> 00:05:33;08
Each factor has it's own sign if you plug in a value and depending on whether it's a
positive or negative value, that will effect your overall product as well.

69
00:05:33;09 --> 00:05:38;08
That's something else to keep in mind. When you guys do a little more practice, I
think you'll get the hang of it.

70
00:05:38;09 --> 00:05:47;14
But, I just wanted to bring that up because we're going to more and more of these that you'll have to start looking really really carefully at, and not assuming too much.