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.