0:00:02.180,0:00:06.158 Completing the square works[br]because you can change one 0:00:06.158,0:00:08.810 parabola into another using[br]standard transformations. 0:00:10.850,0:00:12.580 You can scale the parabola. 0:00:15.020,0:00:17.729 And you can move the parabola or 0:00:17.729,0:00:20.340 translate it. Horizontally. 0:00:22.020,0:00:23.130 All vertically. 0:00:25.700,0:00:29.345 You can also reflect the[br]parabola. That's like a 0:00:29.345,0:00:32.990 scaling, but with the scale[br]factor of minus one. 0:00:35.410,0:00:41.314 Now the standard quadratic[br]expression Y equals X squared 0:00:41.314,0:00:43.282 gives this parabola. 0:00:44.630,0:00:49.162 And any other quadratic will[br]always give a parabola, but it 0:00:49.162,0:00:53.694 will be a different size and be[br]in a different place. 0:00:55.200,0:01:01.833 So to get this new parabola,[br]we take the standard parabola 0:01:01.833,0:01:09.069 and 1st change its eyes instead[br]of Y equals X squared. It's 0:01:09.069,0:01:12.687 now Y equals 1/2 X squared. 0:01:15.770,0:01:22.304 Next we move the parabola[br]sideways instead of Y equals 1/2 0:01:22.304,0:01:27.650 X squared. The ex has become[br]X minus 2. 0:01:30.710,0:01:34.472 And finally we move the parabola 0:01:34.472,0:01:39.883 vertically. We add on one[br]to the formula and that 0:01:39.883,0:01:43.619 gives us the quadratic in[br]completed square form.