Why is completing the square useful and how do you do it?
Completing the square is nice and easy. If you have an equasion of the form x2+ax+b=0 then simply rewrite the equasion in the form (x+a/2)2-(a/2)2 +b=0. This may sound complicated but is we use numbers it becomes alot more simple, for example x2+6x+5=0 will then change to (x+3)2-9+5=ywhich then simplifies to (x+3)2-4=y
This is useful since it is quick to do and easy to see the interceptions with the axis. To find out when it cross's ' y' axis just sub in x=0 . In the previous example that would be (0+3)2-4=y and so 'y' would equal 5. Then to find out where it crosses the 'x' axis you make y=0 and solve for x. So in the earlier example (x+3)2-4=0 would then go to (x+3)2=4 then x+3=+-2 and so 'x' would equal 5 or 1. This very quickly allows us to make a quick sketch of the graph with thekey features.
