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C3 Functions??

Okay so functions is my weakest part of C3. I was doing this solomon paper and I don't really understand the solution for 2a
question: http://www.thomas-reddington.com/uploads/7/7/8/3/778329/c3_qp_solomon_f.pdf
solution:http://www.thomas-reddington.com/uploads/7/7/8/3/778329/c3_ms_solomon_f.pdf
Reply 1
Complete the square?

x^2+2ax+2= (x+a)^2-a^2+2

The graph will have a minimum point at -a^2+2 right (in terms of y)?

So therefore the range must be g(x) => =a^2+2

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