F4.certificate Maths功課-Quadratic Function~~~幫手!!!

1. f(2) + f(-3)
= [2(2)^2 - (2) + 3] + [2(-3)^2 - (-3) + 3]
= [8 - 2 + 3] + [18 + 3 + 3]
= 9 + 27
= 36
2. (a) f(9) = 44
k(9) + 8 = 44
9k = 36
k = 4
(b) f(x) = 86
4x + 8 = 86
4x = 86 - 8 = 78
x = 78 / 4 = 19.5
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For your question in http://hk.knowledge. yahoo.com/question/? qid=7006102805556 ,
Cut a wire of length 80cm into 2 parts,and then change them to square respectively.The length of each side of the smaller is 4x cm.

(a) Respresent the total area of the two spuares A in terms of x.

(b) Find the minmum value of A.
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(a) The length of each side of the larger square
= [80 - 4(4x)] / 4 = (20 - 4x)cm
Therefore A = (4x)^2 + (20 - 4x)^2
= 16x^2 + 400 - 160x + 16x^2
= (32x^2 - 160x + 400)cm^2
(b) A = 32x^2 - 160x + 400
= 32(x^2 - 5x) + 400
= 32[x^2 - 5x + (5 / 2)^2 - (5 / 2)^2] + 400
= 32[x - 5 / 2]^2 - 32 * (25 / 4) + 400
= 32[x - 5 / 2]^2 - 200 + 400
= 32[x - 5 / 2]^2 + 200
Thus the minimum value of A is 200 cm^2

2006-10-29 17:36:45 補充：
For Q1, f(2) + f(-3)= [2(2)^2 - (2) + 3] + [2(-3)^2 - (-3) + 3]= [8 - 2 + 3] + [18 + 3 + 3]= 9 + 24= 33

1)
f(2)+f(-3)
=2(2)^2-(2)+3 + 2(-3)^2-(-3)+3
=9+24
=33

2a)
f(9)=k(9)+8=44
9k=36
k=4

2b)
f(x)=(4)x+8=86
4x=78
x=19.5

1.. f(2)=2*2^2-2+3=9
f(-3)=2*(-3)^2-(-3)+3=24
f(2)+f(-3)=9+24=33

2a.. f(9)=9k+8=44
k=4
b.. f(x)=4x+8
f(x)=86
86=4x+8
x=19.5