Q) The function f is defined by f : x → 2x^2 − 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
(iii) When A has this value, find the range of f
My Attempt
Now I have no clue on how to do (ii) which is linked with (iii). Will appreciated your help!
Thanks!
I guess you can sketch y=x^2 - it goes through (0,0),(1,1),(2,4) (and symmetrically on the left).
The graph of y=2*x^2 is similar, but all points are in the double height -- it goes through (0,0),(1,2),(2,8).
Your function is - so you simply have to move the graph of 3 units to the right and 5 units lower.
(I hope I was able to express myself clearly despite not being native English speaker.)
Yes, the range is correct.
I am definitely not in the position to answer this question. However, the amount of time you spend with a question during a test depends on how much practice you have and whether you have done some similar exercises before. So I think it's good that you're working hard and you're learning things in this forum.