1
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So, let's start with the left one.

2
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In green, what do we call this thing?

3
00:00:12,570 --> 00:00:16,437
And this expression has a special name. What is it called?

4
00:00:19,190 --> 00:00:22,657
Quadratic polynomial. Let's just call it polynomial.

5
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Quadratic refers to a polynomial.

6
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So, we could just call it quadratic.

7
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And then the one in the middle, what do we call it?

8
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Sometimes we might say a quadratic equation in one variable.

9
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It's just a quadratic equation.

10
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And then the third one is what?

11
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Quadratic equation in two variables and we therefore answer y equals or f of x

12
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equals. So, we call it a quadratic function.

13
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They all factor.

14
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x plus 5 times x minus 3.

15
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Zero equals x plus five times x minus three. x plus 5, x minus 3.

16
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And, let me get my colors straight.

17
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f of x equals x plus 5 times x minus 3.

18
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The first line, they're all written in standard form, which is descending order.

19
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This line, they're all written in what form?

20
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Factored form. The leading coefficient for all of them is one.

21
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And from factor form, what can we tell real quick?

22
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This is very important.

23
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And the zeros are? Negative five and three.

24
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Okay, these same numbers here are called something else. What are they called?

25
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They're called solutions.

26
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What is a solution?

27
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A number, when plugged into the equation, makes the equation true.

28
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Yeah, so if it's an equation 1 variable, it's a number, then when replacing the

29
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variable makes the equation true.

30
00:03:01,910 --> 00:03:07,243
Okay, these same two numbers are not solutions here. Why are they not solutions?

31
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It's not an equation.

32
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Okay, and we call these same numbers roots.

33
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Okay.

34
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So they all sort of mean the same thing.

35
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But because we have different things, we have a polynomial or an expression.

36
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We have an equation in 1 variable, we have an equation in 2 variables, or a

37
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function. Functions have zeros.

38
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They also have solutions. Right, negative 5 is zero, but what's the actual solution?

39
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First off, it's an equation in 2 variables, so solutions are not numbers, they're

40
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ordered pairs.

41
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Zeros are x values that make y zero.

42
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Okay, so these do have solutions, they have an infinite number of solutions, but the

43
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two, where the y values are zero, we call them zeros.

44
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Okay, so new word we're learning today is a root.

45
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It's simply if this, it's values of x that make the polynomial, you plug them in

46
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equal to zero.

47
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Okay, or the value is zero. That's what a root is.

48
00:04:32,550 --> 00:04:36,690
Does this have roots, solutions, or zeros?

49
00:04:36,690 --> 00:04:43,839
Zero. It also has solutions, but in this context, we're talking about zeros, and the

50
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zeros are?

51
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Negative 4 and 3.

52
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You can put a comma, you can say and, it doesn't really matter. They're just

53
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numbers.

54
00:04:55,570 --> 00:04:57,810
Okay, and why do we have zeros?

55
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Because it's a function. Okay, it's x values that make f of x zero.

56
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Does this have roots, solutions, or zeros?

57
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And the roots are?

58
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Negative 5 and negative 2.

59
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Okay.

60
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What are we going to call 2 and negative 2 solutions?

61
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Or solutions.

62
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Okay. Equations in one variable have solutions.

63
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Especially when it's just two numbers.

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Okay, so that's the only difference.