00:01
In this problem, we're being asked to graph the system of inequalities.
00:04
Well, let's first start with our, let's begin with the first inequality.
00:07
X squared plus y squared is less than equal to nine.
00:10
Remember, this is the equation for a circle whose center is at the origin.
00:15
And we know it's centered at the origin because it's just x squared and y squared.
00:18
Now remember, the radius will be the square root of our constant at the end.
00:22
Well, the square of the nine is equal to three.
00:24
So if we were to draw this circle, we have our center at the origin, and it's radius is at three.
00:29
So we know four points on it.
00:30
It'd be three units to the right, three units up, three units to the left, and three units down.
00:36
So now that we have these points, we can go ahead and draw our circle.
00:41
Okay, so now let's look at our second inequality.
00:44
Why is less than equal to four minus one half x squared? well, notice we have a quadratic, so we know the shape is going to be a parabola.
00:52
In this case, for transformations, it went up four units.
00:57
Okay, so now that we know it just went up four units, we're going to have a vertical string, a string, and because a is less than zero, we know that it's going to open downwards.
01:06
So we can find a couple of our points by substituting values for x into our function.
01:11
So first off, let's try when x is equal to 1.
01:13
So we would have y equal to 4 minus 1 1⁄2 times 1 squared.
01:18
Well, 1 squared is just 1...