00:01
Okay, i want to find the area between these two parabolas.
00:04
So the first one is just the ordinary parabola, y equals x squared, except for it's screwed it up one.
00:12
Okay, so it looks like this.
00:16
Okay, now the second one is upside down, and i'm not exactly sure where it is.
00:20
So i could do some calculus to it, but instead i'm going to complete the square, but it's tricky.
00:43
Okay, so out of this, negative x squared, i factored a minus, and out of the 2x, i factored a minus.
00:51
So it's minus minus minus.
00:53
And then i'm going to add something in there to complete the square, but i'm not really adding because of this minus sign.
01:01
So i have to add it in here.
01:04
Okay, so half of minus 2 is 1.
01:07
So i really put in minus 1, so i have to add positive 1 here.
01:11
So i get minus x minus 1 squared plus 2.
01:16
Okay, so up to.
01:21
One to the right.
01:25
These should be at their one to the right and then upside down.
01:37
Okay.
01:39
Okay, another way to do it, maybe a simpler way would have just been, take the derivative, which is minus 2x plus 2, set that equal to zero.
01:48
So you get x equals 1.
01:50
So this has a maximum at x equals 1, which is the vertex because it's a parabola.
01:57
So that would have been easier to just do that instead of this weird completing the square...