need help to solve this question. AS MATHS {CIE} m/j2009

[lhl_anecar]

10 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. [3]
(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. [2]
The function g is defined by g : x  ? 2x2 ? 12x + 13 for x ? 4.
(iv) Explain why g has an inverse. [1]
(v) Obtain an expression, in terms of x, for g?1(x). [3]

Answers for (ii) is : symmetrical about x=3 and A=6

can someone explain to me why is it A=6?? I just can't figure it out. Thanks!!!

And how do I solve part (iii) and (iv).

THANKS IN ADVANCE,

[solo_G]

okay here is what i know:
man if u checked the ranges for f(x) using "table" in the calculator u will find it as follows:
X    Y
0    13
1     3
2      -3
3      -5
4       -3
5       3
6        13
u will see that after the turning point the f(x) values started 2 repeat reaching the initial value(13) and since the question specified :from 0 to A then A should be 6 having a f(x) value like 0
for (iii) it could be found wed da calculator like i did at the top so the answer would be -5<Y<13(i used the values i got for substituting the X values)

for (iv) i have only one reason that i copy-paste to all questions of this type:

"since g(x) is a one-to-one function" hope i helped!

[lhl_anecar]

thanks alot. appreciate it !