00:01
Let's go ahead and graph this parabola and based on the graph, we'll make a guess for the x intercepts, and then we'll algebraically find the x intercepts and compare our results.
00:14
So to graph this, one could plot points.
00:19
Another method is just to go ahead and complete the square.
00:24
So i see a 4 here on the x and negative 4.
00:28
You take half of that, which is negative 2, square that.
00:34
You get 4.
00:36
So what i'll do here is i'll add in a 4 and then i'll make up for the adding the 4 by subtracting 4 as well.
00:45
So as you can see, we really haven't changed the expression because these two will just cancel out.
00:54
Now the reason for doing this is that we can go ahead and simplify inside the parentheses and then we get the standard form.
01:07
And the reason the standard form is useful is because if you know how to graph xx4, squared then you see our expression over here will be a shift to the right because we're subtracting two from the x and then also here we'll shift down by 9 and we could see that our vertex is the point 2 negative 9 so let's go ahead and plot that point in there's 2 negative 9 right down here so here's a rough sketch and then we know that in the regular graph of x squared if you go over one unit from the vertex, then the y value goes up by one.
02:15
So we'll use that fact here...