00:01
Okay, so for this question, we want to find the function whose graph is based on this function right here, y equals x squared, but shifted three units to the right, and four units.
00:26
So in order to have this kind of graph, you should maybe try to sketch out what it would look like without the shift.
00:34
So if you have y equals x squared, that's just a regular parabola.
00:37
And we want it so that this parabola shifts over to the right.
00:45
So we want it to shift over this way, three units to the right, and then four units down.
01:04
Let's say that's above.
01:06
So how do we end up doing something like this? well, if you remember how to move something vertically, like with a straight line, say if you had something like y equals x, then all you really had to do to move it up, say you want to move it up three units, you just add three, and then it would go from that to the same graph just shifted up three units.
01:40
Now, since we have a different kind of function here, since it's x squared instead of just x, we have some slightly different rules only for shifting something to the right because when we had y goes x, we weren't really concerned.
01:59
With this because it kind of kind of came along with just moving it up and down.
02:05
But now that we have a parabola or something, because there's more of a shape to it, you kind of have to consider more factors, essentially.
02:14
So if we want to move something up and down, same rules apply.
02:19
You have the parabola here, and you want to move it four units down, you just subtract four from this function here.
02:29
So it would be x squared minus four...