[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:02.18,0:00:06.16,Default,,0000,0000,0000,,Completing the square works\Nbecause you can change one
Dialogue: 0,0:00:06.16,0:00:08.81,Default,,0000,0000,0000,,parabola into another using\Nstandard transformations.
Dialogue: 0,0:00:10.85,0:00:12.58,Default,,0000,0000,0000,,You can scale the parabola.
Dialogue: 0,0:00:15.02,0:00:17.73,Default,,0000,0000,0000,,And you can move the parabola or
Dialogue: 0,0:00:17.73,0:00:20.34,Default,,0000,0000,0000,,translate it. Horizontally.
Dialogue: 0,0:00:22.02,0:00:23.13,Default,,0000,0000,0000,,All vertically.
Dialogue: 0,0:00:25.70,0:00:29.34,Default,,0000,0000,0000,,You can also reflect the\Nparabola. That's like a
Dialogue: 0,0:00:29.34,0:00:32.99,Default,,0000,0000,0000,,scaling, but with the scale\Nfactor of minus one.
Dialogue: 0,0:00:35.41,0:00:41.31,Default,,0000,0000,0000,,Now the standard quadratic\Nexpression Y equals X squared
Dialogue: 0,0:00:41.31,0:00:43.28,Default,,0000,0000,0000,,gives this parabola.
Dialogue: 0,0:00:44.63,0:00:49.16,Default,,0000,0000,0000,,And any other quadratic will\Nalways give a parabola, but it
Dialogue: 0,0:00:49.16,0:00:53.69,Default,,0000,0000,0000,,will be a different size and be\Nin a different place.
Dialogue: 0,0:00:55.20,0:01:01.83,Default,,0000,0000,0000,,So to get this new parabola,\Nwe take the standard parabola
Dialogue: 0,0:01:01.83,0:01:09.07,Default,,0000,0000,0000,,and 1st change its eyes instead\Nof Y equals X squared. It's
Dialogue: 0,0:01:09.07,0:01:12.69,Default,,0000,0000,0000,,now Y equals 1/2 X squared.
Dialogue: 0,0:01:15.77,0:01:22.30,Default,,0000,0000,0000,,Next we move the parabola\Nsideways instead of Y equals 1/2
Dialogue: 0,0:01:22.30,0:01:27.65,Default,,0000,0000,0000,,X squared. The ex has become\NX minus 2.
Dialogue: 0,0:01:30.71,0:01:34.47,Default,,0000,0000,0000,,And finally we move the parabola
Dialogue: 0,0:01:34.47,0:01:39.88,Default,,0000,0000,0000,,vertically. We add on one\Nto the formula and that
Dialogue: 0,0:01:39.88,0:01:43.62,Default,,0000,0000,0000,,gives us the quadratic in\Ncompleted square form.