Question 183458
In order to get {{{x^2-6x+5}}} into vertex form, we need to complete the square:



{{{x^2-6x+5}}} Start with the given expression.



Take half of the {{{x}}} coefficient {{{-6}}} to get {{{-3}}}. In other words, {{{(1/2)(-6)=-3}}}.



Now square {{{-3}}} to get {{{9}}}. In other words, {{{(-3)^2=(-3)(-3)=9}}}



{{{x^2-6x+highlight(9-9)+5}}} Now add <font size=4><b>and</b></font> subtract {{{9}}}. Make sure to place this after the "x" term. Notice how {{{9-9=0}}}. So the expression is not changed.



{{{(x^2-6x+9)-9+5}}} Group the first three terms.



{{{(x-3)^2-9+5}}} Factor {{{x^2-6x+9}}} to get {{{(x-3)^2}}}.



{{{(x-3)^2-4}}} Combine like terms.



So after completing the square, {{{x^2-6x+5}}} transforms to {{{(x-3)^2-4}}}. 



Now the expression {{{(x-3)^2-4}}} is in vertex form.