2022 SQA Higher Mathematics Paper 1 no.11 Completing the square

This is quite long as four different methods have been used to complete the square of a given quadratic expression.

This is an instructional exercise consisting of question 11 from the first paper of the 2022 SQA New Higher Mathematics examination.

Where appropriate the alternative methods for solving the problem are also given.
Set out in stages of 'try then check' the worked solution to each part of the question.
Including indications of where each mark is allocated, and the requirements for that mark, according to the marking scheme.