f.4 maths_11－航空百大

標題:

f.4 maths

發問:

1.find the optimum value and the axis of symmetry of y=-2x^2+4x+7 2.a rectangle BDEF of length x cm is inscried in a right-angled triangle ABC,where AB=16cm and BC=12cm. (a)find the length EF and the area of BDEF in terms of x (b)find the area of the largest rectangle that can be inscribed in triangle ABC.

最佳解答:

1.y = -2x2+4x+7 = -2(x2﹣2x)+7 = -2[x2﹣2x+ (2/2)2﹣(2/2)2]+7 = -2(x﹣1)2+2+7 = -2(x﹣1)2+9 ∴the maximum value is 9, the axis of symmetry is x = 1 2(a)DE:AB = CD:CB x/8 = (6﹣EF)/6 6x = 48﹣8EF EF = (48﹣6x)/8 = 6﹣(3x/4)cm the area of BDEF = x(6﹣2x/3) cm2 = (-3x2/4 + 6x) cm2 (b)Let y be the area of BDEF, y = -3x2/4 + 6x = -3/4(x2﹣8x) = -3/4[x2﹣8x+(8/2)2﹣(8/2)2] =-3/4 (x﹣4)2 + 12 ∴the area of the largest rectangle is 12cm2

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