Video Transcript
Sketch the graph of ๐ of ๐ฅ equals negative ๐ฅ minus one squared ๐ฅ plus one squared.
So before we sketch the graph, letโs look at some features. If we would multiply all of this out, the leading coefficient would be a negative ๐ฅ to the fourth. So it would have a degree of four, so it will be an even function with a negative leading coefficient.
So if itโs even with a negative leading coefficient, the arrows will go downwards. Looking at the factors, if we would set those equal to zero, we will know where we cross the ๐ฅ-axis. So we will cross out one and negative one; however, we also need to look at the multiplicity of these factors.
Since each of them are squared, they have an even multiplicity. So instead of crossing through at that point, it will actually bounce off of that point. So at one and negative one, we wonโt go through them; we will bounce off of them.
And we know our arrow should be facing downwards. So as I begin to draw this, instead of going through, we will bounce off, and same with the other one, and we go back down. So this would be the sketch of that graph.
