f.4 maths ,,help

f ( x ) =8x 2次+2x+3
f(k+3)
=8(k+3)^2+2(k+3)+3
=8(k^2+6k+9)+2k+6+3
=8k^2+48k+72+2k+6+3
=8k^2+50k+81
f(k+2)
8(k+2)^2+2(k+2)+3
=8(k^2+4k+4)+2k+4+3
=8k^2+32k+32+2k+4+3
=8k^2+34k+39
f(k+3)-f(k+2)
=(8k^2+50k+81)-(8k^2+34k+39)
=16k+42

一條函數問題

f(x) = 8 x^2 + 2x + 3

f(k+3)既意思係要係將公式上原本係 "x" 既野變晒做 "k+3"
f(k+2)既意思係要係將公式上原本係 "x" 既野變晒做 "k+2"

即 [8 (k+3)^2 + 2(k+3) + 3] - [8 (k+2)^2 + 2(k+2) + 3]
= [8 (k^2 + 6k + 9) + 2k + 6 + 3] - [8 (k^2 + 4k + 4) + 2k + 4 + 3]
= 8k^2 + 48k + 72 +2k + 6 +3 - 8k^2 - 32k - 32 - 2k - 4 - 3
= 16k + 42
= 2 (8k + 21)

當然, 以上只係一個最傳統既計法.
仲有一個快d既方法, 想知就再問啦.

f(k+3) = 8(k+3)^2 + 2(k+3) +3
=8k^2 + 48k + 72 + 2k + 6 + 3
= 8k^2 + 50k + 81

f(k+2) = 8(k+2)^2 + 2(k+2) +3
=8k^2 + 32k + 32 + 2k + 4 + 3
= 8k^2 + 34k + 39

f(k+3)-f(k+2) = 8k^2 + 50k + 81 - 8k^2 + 34k + 39
= 16k + 42

2006-10-22 23:16:46 補充：
miss ( )f(k+3)-f(k+2) = 8k^2 + 50k + 81 - (8k^2 + 34k + 39)= 16k + 42