1 00:00:02,180 --> 00:00:06,158 Completing the square works because you can change one 2 00:00:06,158 --> 00:00:08,810 parabola into another using standard transformations. 3 00:00:10,850 --> 00:00:12,580 You can scale the parabola. 4 00:00:15,020 --> 00:00:17,729 And you can move the parabola or 5 00:00:17,729 --> 00:00:20,340 translate it. Horizontally. 6 00:00:22,020 --> 00:00:23,130 All vertically. 7 00:00:25,700 --> 00:00:29,345 You can also reflect the parabola. That's like a 8 00:00:29,345 --> 00:00:32,990 scaling, but with the scale factor of minus one. 9 00:00:35,410 --> 00:00:41,314 Now the standard quadratic expression Y equals X squared 10 00:00:41,314 --> 00:00:43,282 gives this parabola. 11 00:00:44,630 --> 00:00:49,162 And any other quadratic will always give a parabola, but it 12 00:00:49,162 --> 00:00:53,694 will be a different size and be in a different place. 13 00:00:55,200 --> 00:01:01,833 So to get this new parabola, we take the standard parabola 14 00:01:01,833 --> 00:01:09,069 and 1st change its eyes instead of Y equals X squared. It's 15 00:01:09,069 --> 00:01:12,687 now Y equals 1/2 X squared. 16 00:01:15,770 --> 00:01:22,304 Next we move the parabola sideways instead of Y equals 1/2 17 00:01:22,304 --> 00:01:27,650 X squared. The ex has become X minus 2. 18 00:01:30,710 --> 00:01:34,472 And finally we move the parabola 19 00:01:34,472 --> 00:01:39,883 vertically. We add on one to the formula and that 20 00:01:39,883 --> 00:01:43,619 gives us the quadratic in completed square form.