AMATH..

since the answers of a) should be : A( -2, 2) & B(6,22)

and C(1,-7) where f(x) = x^2 - 2x - 6 = (x-1) ^2 -7

as shown the C pt is on the right hand side of y-axis

and then b)

you could see from the Figure 3 that

f(x) =< g(x) if -2 =< x =< 6

Hence ,

f(x) = k where x has only 1 real root

that is f(x) - k = 0

choose k = -7 which y = -7 meet at only the vertex of y = f(x) .

This choose does not depend on the range of x in between (-2,6).

2nd method

you could directly solve out : f(x) - k =0 as finding its discriminate which set it to be 0 and finally solve out the k 's value . the result is also equal to -7.

2006-12-14 22:46:07 補充：
Some mistakessince y = f(x) is symmetirc about the veritcal line : x = 1and if conside only x in [ -2 , 6 ]y = k for 4 =< k =< 6then y = k and y = f(x) meet at only one pt also.Therefore , the correct answer of k should be k=-7 or 4 =< k =< 6

紅框個度比較陰險
個度話k得一個值
咁除c點還有一d數係可以令f(x) </= g(x)且f(x)係一個解
由a點畫一條水平線連接右邊
會發覺右既上方係會同時可以令f(x) </= g(x)且f(x)係一個解
所以紅框既答案好自然出現
有咩唔明再問我~