00:01
So this question asks us to take a particular function, g of x equals x squared minus 8x, and find its vertex, sketch the function, but also write it in standard form.
00:11
Now, if you recall, standard form is of the form f of x is equal to some constant a times x minus h squared plus k, where h and k are numbers.
00:26
But what makes it easy is that the vertex is the point hk.
00:33
So that's the advantage of having this form.
00:35
Now, in this particular case, we don't have an a.
00:38
But what i'm going to do to get this g of x into this form is i'm going to add 16 to both sides.
00:46
And you'll see why i do that, because what we've got is g of x plus 16 is now x squared minus 8x plus 16.
00:55
Now we know that this is a perfect square, and it's x, excuse me, x minus 4, quantity squared.
01:03
So now all we have to do to get this back into standard form is move this 16 over, so i'm going to do that in the next step.
01:09
So g of x equals x minus 4 quantity squared minus 16.
01:16
And that is our function in standard form.
01:18
Now let's quickly sketch the graph, so we know that it's to the right form.
01:28
So let's take our parent function, which would be something like this...