[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.01,0:00:04.52,Default,,0000,0000,0000,,Welcome to the presentation on\Nusing the quadratic equation.
Dialogue: 0,0:00:04.52,0:00:06.73,Default,,0000,0000,0000,,So the quadratic equation,\Nit sounds like something
Dialogue: 0,0:00:06.73,0:00:07.81,Default,,0000,0000,0000,,very complicated.
Dialogue: 0,0:00:07.81,0:00:09.93,Default,,0000,0000,0000,,And when you actually first see\Nthe quadratic equation, you'll
Dialogue: 0,0:00:09.93,0:00:11.59,Default,,0000,0000,0000,,say, well, not only does it\Nsound like something
Dialogue: 0,0:00:11.59,0:00:13.11,Default,,0000,0000,0000,,complicated, but it is\Nsomething complicated.
Dialogue: 0,0:00:13.11,0:00:14.93,Default,,0000,0000,0000,,But hopefully you'll see,\Nover the course of this
Dialogue: 0,0:00:14.93,0:00:16.58,Default,,0000,0000,0000,,presentation, that it's\Nactually not hard to use.
Dialogue: 0,0:00:16.58,0:00:19.04,Default,,0000,0000,0000,,And in a future presentation\NI'll actually show you
Dialogue: 0,0:00:19.04,0:00:21.30,Default,,0000,0000,0000,,how it was derived.
Dialogue: 0,0:00:21.30,0:00:24.81,Default,,0000,0000,0000,,So, in general, you've already\Nlearned how to factor a
Dialogue: 0,0:00:24.81,0:00:25.81,Default,,0000,0000,0000,,second degree equation.
Dialogue: 0,0:00:25.81,0:00:30.91,Default,,0000,0000,0000,,You've learned that if I\Nhad, say, x squared minus
Dialogue: 0,0:00:30.91,0:00:40.34,Default,,0000,0000,0000,,x, minus 6, equals 0.
Dialogue: 0,0:00:40.34,0:00:42.97,Default,,0000,0000,0000,,If I had this equation. x\Nsquared minus x minus x equals
Dialogue: 0,0:00:42.97,0:00:48.72,Default,,0000,0000,0000,,zero, that you could factor\Nthat as x minus 3 and
Dialogue: 0,0:00:48.72,0:00:52.21,Default,,0000,0000,0000,,x plus 2 equals 0.
Dialogue: 0,0:00:52.21,0:00:54.96,Default,,0000,0000,0000,,Which either means that\Nx minus 3 equals 0 or
Dialogue: 0,0:00:54.96,0:00:57.07,Default,,0000,0000,0000,,x plus 2 equals 0.
Dialogue: 0,0:00:57.07,0:01:03.51,Default,,0000,0000,0000,,So x minus 3 equals 0\Nor x plus 2 equals 0.
Dialogue: 0,0:01:03.51,0:01:08.50,Default,,0000,0000,0000,,So, x equals 3 or negative 2.
Dialogue: 0,0:01:08.50,0:01:17.98,Default,,0000,0000,0000,,And, a graphical representation\Nof this would be, if I had the
Dialogue: 0,0:01:17.98,0:01:26.15,Default,,0000,0000,0000,,function f of x is equal to\Nx squared minus x minus 6.
Dialogue: 0,0:01:26.15,0:01:28.76,Default,,0000,0000,0000,,So this axis is\Nthe f of x axis.
Dialogue: 0,0:01:28.76,0:01:32.67,Default,,0000,0000,0000,,You might be more familiar with\Nthe y axis, and for the purpose
Dialogue: 0,0:01:32.67,0:01:34.78,Default,,0000,0000,0000,,of this type of problem,\Nit doesn't matter.
Dialogue: 0,0:01:34.78,0:01:36.27,Default,,0000,0000,0000,,And this is the x axis.
Dialogue: 0,0:01:36.27,0:01:40.43,Default,,0000,0000,0000,,And if I were to graph this\Nequation, x squared minus x,
Dialogue: 0,0:01:40.43,0:01:42.38,Default,,0000,0000,0000,,minus 6, it would look\Nsomething like this.
Dialogue: 0,0:01:42.38,0:01:50.13,Default,,0000,0000,0000,,A bit like -- this is f\Nof x equals minus 6.
Dialogue: 0,0:01:50.13,0:01:52.90,Default,,0000,0000,0000,,And the graph will kind of\Ndo something like this.
Dialogue: 0,0:01:52.90,0:01:57.15,Default,,0000,0000,0000,,\N34\N00:01:57,15 --> 00:02:00,03\NGo up, it will keep going\Nup in that direction.
Dialogue: 0,0:02:00.03,0:02:03.15,Default,,0000,0000,0000,,And know it goes through minus\N6, because when x equals 0,
Dialogue: 0,0:02:03.15,0:02:05.11,Default,,0000,0000,0000,,f of x is equal to minus 6.
Dialogue: 0,0:02:05.11,0:02:07.80,Default,,0000,0000,0000,,So I know it goes\Nthrough this point.
Dialogue: 0,0:02:07.80,0:02:11.52,Default,,0000,0000,0000,,And I know that when f of x is\Nequal to 0, so f of x is equal
Dialogue: 0,0:02:11.52,0:02:14.96,Default,,0000,0000,0000,,to 0 along the x axis, right?
Dialogue: 0,0:02:14.96,0:02:16.60,Default,,0000,0000,0000,,Because this is 1.
Dialogue: 0,0:02:16.60,0:02:17.87,Default,,0000,0000,0000,,This is 0.
Dialogue: 0,0:02:17.87,0:02:19.16,Default,,0000,0000,0000,,This is negative 1.
Dialogue: 0,0:02:19.16,0:02:21.51,Default,,0000,0000,0000,,So this is where f of x\Nis equal to 0, along
Dialogue: 0,0:02:21.51,0:02:23.42,Default,,0000,0000,0000,,this x axis, right?
Dialogue: 0,0:02:23.42,0:02:29.21,Default,,0000,0000,0000,,And we know it equals 0 at the\Npoints x is equal to 3 and
Dialogue: 0,0:02:29.21,0:02:32.33,Default,,0000,0000,0000,,x is equal to minus 2.
Dialogue: 0,0:02:32.33,0:02:34.36,Default,,0000,0000,0000,,That's actually what\Nwe solved here.
Dialogue: 0,0:02:34.36,0:02:36.44,Default,,0000,0000,0000,,Maybe when we were doing the\Nfactoring problems we didn't
Dialogue: 0,0:02:36.44,0:02:38.94,Default,,0000,0000,0000,,realize graphically\Nwhat we were doing.
Dialogue: 0,0:02:38.94,0:02:42.07,Default,,0000,0000,0000,,But if we said that f of x is\Nequal to this function, we're
Dialogue: 0,0:02:42.07,0:02:43.27,Default,,0000,0000,0000,,setting that equal to 0.
Dialogue: 0,0:02:43.27,0:02:44.82,Default,,0000,0000,0000,,So we're saying this\Nfunction, when does
Dialogue: 0,0:02:44.82,0:02:48.22,Default,,0000,0000,0000,,this function equal 0?
Dialogue: 0,0:02:48.22,0:02:49.39,Default,,0000,0000,0000,,When is it equal to 0?
Dialogue: 0,0:02:49.39,0:02:51.72,Default,,0000,0000,0000,,Well, it's equal to 0 at\Nthese points, right?
Dialogue: 0,0:02:51.72,0:02:55.36,Default,,0000,0000,0000,,Because this is where\Nf of x is equal to 0.
Dialogue: 0,0:02:55.36,0:02:57.49,Default,,0000,0000,0000,,And then what we were doing\Nwhen we solved this by
Dialogue: 0,0:02:57.49,0:03:01.97,Default,,0000,0000,0000,,factoring is, we figured out,\Nthe x values that made f of x
Dialogue: 0,0:03:01.97,0:03:04.16,Default,,0000,0000,0000,,equal to 0, which is\Nthese two points.
Dialogue: 0,0:03:04.16,0:03:06.74,Default,,0000,0000,0000,,And, just a little terminology,\Nthese are also called
Dialogue: 0,0:03:06.74,0:03:09.86,Default,,0000,0000,0000,,the zeroes, or the\Nroots, of f of x.
Dialogue: 0,0:03:09.86,0:03:12.47,Default,,0000,0000,0000,,\N63\N00:03:12,47 --> 00:03:14,81\NLet's review that a little bit.
Dialogue: 0,0:03:14.81,0:03:23.70,Default,,0000,0000,0000,,So, if I had something like f\Nof x is equal to x squared plus
Dialogue: 0,0:03:23.70,0:03:29.55,Default,,0000,0000,0000,,4x plus 4, and I asked you,\Nwhere are the zeroes, or
Dialogue: 0,0:03:29.55,0:03:31.77,Default,,0000,0000,0000,,the roots, of f of x.
Dialogue: 0,0:03:31.77,0:03:33.97,Default,,0000,0000,0000,,That's the same thing as\Nsaying, where does f of x
Dialogue: 0,0:03:33.97,0:03:36.30,Default,,0000,0000,0000,,interject intersect the x axis?
Dialogue: 0,0:03:36.30,0:03:38.21,Default,,0000,0000,0000,,And it intersects the\Nx axis when f of x is
Dialogue: 0,0:03:38.21,0:03:39.44,Default,,0000,0000,0000,,equal to 0, right?
Dialogue: 0,0:03:39.44,0:03:42.12,Default,,0000,0000,0000,,If you think about the\Ngraph I had just drawn.
Dialogue: 0,0:03:42.12,0:03:45.72,Default,,0000,0000,0000,,So, let's say if f of x is\Nequal to 0, then we could
Dialogue: 0,0:03:45.72,0:03:51.86,Default,,0000,0000,0000,,just say, 0 is equal to x\Nsquared plus 4x plus 4.
Dialogue: 0,0:03:51.86,0:03:53.94,Default,,0000,0000,0000,,And we know, we could just\Nfactor that, that's x
Dialogue: 0,0:03:53.94,0:03:57.08,Default,,0000,0000,0000,,plus 2 times x plus 2.
Dialogue: 0,0:03:57.08,0:04:07.09,Default,,0000,0000,0000,,And we know that it's equal\Nto 0 at x equals minus 2.
Dialogue: 0,0:04:07.09,0:04:10.17,Default,,0000,0000,0000,,\N78\N00:04:10,17 --> 00:04:13,94\Nx equals minus 2.
Dialogue: 0,0:04:13.94,0:04:18.27,Default,,0000,0000,0000,,Well, that's a little\N-- x equals minus 2.
Dialogue: 0,0:04:18.27,0:04:22.38,Default,,0000,0000,0000,,So now, we know how to find\Nthe 0's when the the actual
Dialogue: 0,0:04:22.38,0:04:24.56,Default,,0000,0000,0000,,equation is easy to factor.
Dialogue: 0,0:04:24.56,0:04:27.50,Default,,0000,0000,0000,,But let's do a situation where\Nthe equation is actually
Dialogue: 0,0:04:27.50,0:04:28.85,Default,,0000,0000,0000,,not so easy to factor.
Dialogue: 0,0:04:28.85,0:04:32.12,Default,,0000,0000,0000,,\N85\N00:04:32,12 --> 00:04:39,75\NLet's say we had f of x\Nis equal to minus 10x
Dialogue: 0,0:04:39.75,0:04:45.38,Default,,0000,0000,0000,,squared minus 9x plus 1.
Dialogue: 0,0:04:45.38,0:04:47.58,Default,,0000,0000,0000,,Well, when I look at this, even\Nif I were to divide it by 10 I
Dialogue: 0,0:04:47.58,0:04:48.65,Default,,0000,0000,0000,,would get some fractions here.
Dialogue: 0,0:04:48.65,0:04:53.13,Default,,0000,0000,0000,,And it's very hard to imagine\Nfactoring this quadratic.
Dialogue: 0,0:04:53.13,0:04:54.86,Default,,0000,0000,0000,,And that's what's actually\Ncalled a quadratic equation, or
Dialogue: 0,0:04:54.86,0:04:57.58,Default,,0000,0000,0000,,this second degree polynomial.
Dialogue: 0,0:04:57.58,0:04:59.60,Default,,0000,0000,0000,,But let's set it -- So we're\Ntrying to solve this.
Dialogue: 0,0:04:59.60,0:05:02.42,Default,,0000,0000,0000,,Because we want to find\Nout when it equals 0.
Dialogue: 0,0:05:02.42,0:05:07.13,Default,,0000,0000,0000,,Minus 10x squared\Nminus 9x plus 1.
Dialogue: 0,0:05:07.13,0:05:09.09,Default,,0000,0000,0000,,We want to find out what\Nx values make this
Dialogue: 0,0:05:09.09,0:05:11.26,Default,,0000,0000,0000,,equation equal to zero.
Dialogue: 0,0:05:11.26,0:05:13.73,Default,,0000,0000,0000,,And here we can use a tool\Ncalled a quadratic equation.
Dialogue: 0,0:05:13.73,0:05:15.62,Default,,0000,0000,0000,,And now I'm going to give you\None of the few things in math
Dialogue: 0,0:05:15.62,0:05:18.03,Default,,0000,0000,0000,,that's probably a good\Nidea to memorize.
Dialogue: 0,0:05:18.03,0:05:21.33,Default,,0000,0000,0000,,The quadratic equation says\Nthat the roots of a quadratic
Dialogue: 0,0:05:21.33,0:05:24.81,Default,,0000,0000,0000,,are equal to -- and let's say\Nthat the quadratic equation is
Dialogue: 0,0:05:24.81,0:05:31.90,Default,,0000,0000,0000,,a x squared plus b\Nx plus c equals 0.
Dialogue: 0,0:05:31.90,0:05:35.79,Default,,0000,0000,0000,,So, in this example,\Na is minus 10.
Dialogue: 0,0:05:35.79,0:05:39.94,Default,,0000,0000,0000,,b is minus 9, and c is 1.
Dialogue: 0,0:05:39.94,0:05:48.04,Default,,0000,0000,0000,,The formula is the roots x\Nequals negative b plus or minus
Dialogue: 0,0:05:48.04,0:05:58.06,Default,,0000,0000,0000,,the square root of b squared\Nminus 4 times a times c,
Dialogue: 0,0:05:58.06,0:06:00.23,Default,,0000,0000,0000,,all of that over 2a.
Dialogue: 0,0:06:00.23,0:06:02.84,Default,,0000,0000,0000,,I know that looks complicated,\Nbut the more you use it, you'll
Dialogue: 0,0:06:02.84,0:06:04.40,Default,,0000,0000,0000,,see it's actually not that bad.
Dialogue: 0,0:06:04.40,0:06:07.72,Default,,0000,0000,0000,,And this is a good\Nidea to memorize.
Dialogue: 0,0:06:07.72,0:06:10.73,Default,,0000,0000,0000,,So let's apply the quadratic\Nequation to this equation
Dialogue: 0,0:06:10.73,0:06:12.67,Default,,0000,0000,0000,,that we just wrote down.
Dialogue: 0,0:06:12.67,0:06:15.26,Default,,0000,0000,0000,,So, I just said -- and look,\Nthe a is just the coefficient
Dialogue: 0,0:06:15.26,0:06:18.61,Default,,0000,0000,0000,,on the x term, right?
Dialogue: 0,0:06:18.61,0:06:20.30,Default,,0000,0000,0000,,a is the coefficient on\Nthe x squared term.
Dialogue: 0,0:06:20.30,0:06:23.57,Default,,0000,0000,0000,,b is the coefficient on the x\Nterm, and c is the constant.
Dialogue: 0,0:06:23.57,0:06:25.10,Default,,0000,0000,0000,,So let's apply it\Ntot this equation.
Dialogue: 0,0:06:25.10,0:06:26.25,Default,,0000,0000,0000,,What's b?
Dialogue: 0,0:06:26.25,0:06:28.70,Default,,0000,0000,0000,,Well, b is negative 9.
Dialogue: 0,0:06:28.70,0:06:29.97,Default,,0000,0000,0000,,We could see here.
Dialogue: 0,0:06:29.97,0:06:33.98,Default,,0000,0000,0000,,b is negative 9, a\Nis negative 10.
Dialogue: 0,0:06:33.98,0:06:34.97,Default,,0000,0000,0000,,c is 1.
Dialogue: 0,0:06:34.97,0:06:36.09,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:36.09,0:06:42.35,Default,,0000,0000,0000,,So if b is negative 9 -- so\Nlet's say, that's negative 9.
Dialogue: 0,0:06:42.35,0:06:49.26,Default,,0000,0000,0000,,Plus or minus the square\Nroot of negative 9 squared.
Dialogue: 0,0:06:49.26,0:06:49.81,Default,,0000,0000,0000,,Well, that's 81.
Dialogue: 0,0:06:49.81,0:06:53.14,Default,,0000,0000,0000,,\N128\N00:06:53,14 --> 00:06:56,94\NMinus 4 times a.
Dialogue: 0,0:06:56.94,0:06:59.76,Default,,0000,0000,0000,,a is minus 10.
Dialogue: 0,0:06:59.76,0:07:03.24,Default,,0000,0000,0000,,Minus 10 times c, which is 1.
Dialogue: 0,0:07:03.24,0:07:05.11,Default,,0000,0000,0000,,I know this is messy,\Nbut hopefully you're
Dialogue: 0,0:07:05.11,0:07:06.47,Default,,0000,0000,0000,,understanding it.
Dialogue: 0,0:07:06.47,0:07:09.56,Default,,0000,0000,0000,,And all of that over 2 times a.
Dialogue: 0,0:07:09.56,0:07:14.05,Default,,0000,0000,0000,,Well, a is minus 10, so\N2 times a is minus 20.
Dialogue: 0,0:07:14.05,0:07:14.99,Default,,0000,0000,0000,,So let's simplify that.
Dialogue: 0,0:07:14.99,0:07:19.41,Default,,0000,0000,0000,,Negative times negative\N9, that's positive 9.
Dialogue: 0,0:07:19.41,0:07:26.46,Default,,0000,0000,0000,,Plus or minus the\Nsquare root of 81.
Dialogue: 0,0:07:26.46,0:07:30.66,Default,,0000,0000,0000,,We have a negative 4\Ntimes a negative 10.
Dialogue: 0,0:07:30.66,0:07:31.87,Default,,0000,0000,0000,,This is a minus 10.
Dialogue: 0,0:07:31.87,0:07:33.28,Default,,0000,0000,0000,,I know it's very messy,\NI really apologize
Dialogue: 0,0:07:33.28,0:07:34.38,Default,,0000,0000,0000,,for that, times 1.
Dialogue: 0,0:07:34.38,0:07:39.41,Default,,0000,0000,0000,,So negative 4 times negative\N10 is 40, positive 40.
Dialogue: 0,0:07:39.41,0:07:41.04,Default,,0000,0000,0000,,Positive 40.
Dialogue: 0,0:07:41.04,0:07:46.07,Default,,0000,0000,0000,,And then we have all of\Nthat over negative 20.
Dialogue: 0,0:07:46.07,0:07:48.30,Default,,0000,0000,0000,,Well, 81 plus 40 is 121.
Dialogue: 0,0:07:48.30,0:07:52.33,Default,,0000,0000,0000,,So this is 9 plus or\Nminus the square root
Dialogue: 0,0:07:52.33,0:07:58.29,Default,,0000,0000,0000,,of 121 over minus 20.
Dialogue: 0,0:07:58.29,0:08:01.62,Default,,0000,0000,0000,,Square root of 121 is 11.
Dialogue: 0,0:08:01.62,0:08:03.17,Default,,0000,0000,0000,,So I'll go here.
Dialogue: 0,0:08:03.17,0:08:06.18,Default,,0000,0000,0000,,Hopefully you won't lose\Ntrack of what I'm doing.
Dialogue: 0,0:08:06.18,0:08:13.72,Default,,0000,0000,0000,,So this is 9 plus or\Nminus 11, over minus 20.
Dialogue: 0,0:08:13.72,0:08:19.09,Default,,0000,0000,0000,,And so if we said 9 plus 11\Nover minus 20, that is 9
Dialogue: 0,0:08:19.09,0:08:22.54,Default,,0000,0000,0000,,plus 11 is 20, so this\Nis 20 over minus 20.
Dialogue: 0,0:08:22.54,0:08:23.73,Default,,0000,0000,0000,,Which equals negative 1.
Dialogue: 0,0:08:23.73,0:08:24.90,Default,,0000,0000,0000,,So that's one root.
Dialogue: 0,0:08:24.90,0:08:28.26,Default,,0000,0000,0000,,That's 9 plus -- because\Nthis is plus or minus.
Dialogue: 0,0:08:28.26,0:08:33.79,Default,,0000,0000,0000,,And the other root would be 9\Nminus 11 over negative 20.
Dialogue: 0,0:08:33.79,0:08:37.72,Default,,0000,0000,0000,,Which equals minus\N2 over minus 20.
Dialogue: 0,0:08:37.72,0:08:40.70,Default,,0000,0000,0000,,Which equals 1 over 10.
Dialogue: 0,0:08:40.70,0:08:42.69,Default,,0000,0000,0000,,So that's the other root.
Dialogue: 0,0:08:42.69,0:08:48.95,Default,,0000,0000,0000,,So if we were to graph this\Nequation, we would see that it
Dialogue: 0,0:08:48.95,0:08:52.64,Default,,0000,0000,0000,,actually intersects the x axis.
Dialogue: 0,0:08:52.64,0:08:57.77,Default,,0000,0000,0000,,Or f of x equals 0 at the\Npoint x equals negative
Dialogue: 0,0:08:57.77,0:09:01.69,Default,,0000,0000,0000,,1 and x equals 1/10.
Dialogue: 0,0:09:01.69,0:09:04.08,Default,,0000,0000,0000,,I'm going to do a lot more\Nexamples in part 2, because I
Dialogue: 0,0:09:04.08,0:09:06.10,Default,,0000,0000,0000,,think, if anything, I might\Nhave just confused
Dialogue: 0,0:09:06.10,0:09:08.12,Default,,0000,0000,0000,,you with this one.
Dialogue: 0,0:09:08.12,0:09:11.68,Default,,0000,0000,0000,,So, I'll see you in the\Npart 2 of using the
Dialogue: 0,0:09:11.68,0:09:12.15,Default,,0000,0000,0000,,quadratic equation.
Dialogue: 0,0:09:12.15,0:09:14.08,Default,,0000,0000,0000,,\N