A level Maths Cie S2009 Q10

[Lilyy]

The function f is defined by f : x → 2x²− 12x + 13 for 0 ≤ x ≤ A, where A is a constant
i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.
ii) State the value of A for which the graph of y = f(x) has a line of symmetry
I have no clue on how to do (ii). Will appreciated your help!

 

[Dr.Peterson]

Please show your work and result for (i), so we can help you from there.

Also tell us what you think it means for the graph to have a line of symmetry.

 

[HallsofIvy]

The first part, which you apparently were able to do is just "completing the square". For the second part, (x- a)^2+ b has line of symmetry x= a.