00:01
Okay, let's graph these four examples one at a time.
00:03
So a is a vertical line.
00:06
If i see an inequality or an equation with just x, that's a vertical line.
00:14
So negative 2 would be about here.
00:18
It's less than, not less than or equal to, so it would be a dotted or a dashed line.
00:27
And if i'm shading less than that, then i would be shading to the left.
00:39
So that's a.
00:39
So hang in there.
00:45
We're going to erase and we're going to do b.
00:49
So b is two separate equations.
00:53
We're going to graph them both on the same plane.
01:02
So the first one is a vertical line and the second is a horizontal line.
01:13
When i have just y, that's a horizontal line.
01:17
So the vertical line is between negative 3 and 3.
01:22
So let's do negative 3 here, 3 here.
01:27
So on negative 3, i'm going to have a solid line.
01:34
And on positive 3, i'm going to have a dashed line.
01:43
And just keep in mind, these symbols would give me solid lines.
01:49
This or this gives me a dotted line.
01:55
So my x values are between those two.
01:59
I'm not going to shade it yet because my final answer is going to be where these things overlap.
02:06
My horizontal lines are between zero, so a solid line on zero.
02:14
Let's call this 2.
02:16
A dashed line on 2.
02:21
And i'm between those, so i'm between here and here.
02:26
So where do those systems overlap is really what i'm looking at.
02:31
And that's going to be the area, this small rectangle right there.
02:40
And that would be my solution.
02:44
Okay, let's erase and do c.
02:47
So c is a quadratic, so it's going to have the shape of a parabola, hang tight.
03:01
Now before i graph it, i want to get that y by itself, so i have to do a little algebra.
03:10
So if i'm starting with y minus 1 is less than or equal to x squared, i'm going to add 1 to both sides.
03:20
And y is less than or equal to x squared plus 1.
03:25
So x squared plus 1 is going to be, have a vertex right here at 0, 1...