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Rewrite \(y = {x^2} - 6x + 11\) in the form \(y = {(x - b)^2} + c\).

To get \(b\) (the number inside the bracket), halve the coefficient (number in front) of the second term in the original equation.

Half of -6 is -3 so the bracket becomes \((x-3)\).

\(y = {(x - 3)^2} - 9 + 11\)

\(y = {(x - 3)^2} + 2\)

\(x^{2}-6x\) is not the same as \((x-3)^{2}\).

Expanding \({(x - 3)^2}\), we get:

\(= (x - 3)(x - 3)\)

\(= {x^2} - 3x - 3x + 9\)

\(= {x^2} - 6x + 9\)

So the \({x^2} - 6x\) matches the first two terms from the original equation and we have also added on an extra \(9\) from this squared bracket.

We then combine it with the +11 to get the final answer \(y = {(x - 3)^2} + 2\).