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The figure shows the graph of the parabola y=2x^2－12x which cuts the x-axis at the origin O and at N. ABCD is a rectangle, where A and B are points on thex-axisand C and D are points on the parabola. (a) Find the coordinates of N Sol 2x^2－12x=0 x(x－6)=0 x=0 or x=6 N(6，0) (b) Letthe coordinate of A be (k，0) (i)Write down thecoordinates of B and D Sol A(k，0) 設B(p，0) k－0=6－p p=6－k B(6－k，0) D(k，2k^2－12k) (ii) Find the area of ABCD in terms of k Sol area of ABCD=(－2k^2+12k)*(6－2k) (iii)If the area of ABCD is32，find all possible values of k Sol (－2k^2+12k)*(6－2k)=32 (－k^2+6k)(3－k)=8 －3k^2+k^3+18k－6k^2=8 k^3－9k^2+18k－8=0 (k^2－7k+4)(k－2)=0 k=(7+√33)/2(不合) or k=(7－√33)/2 or k=2
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圖片參考：http://imgcld.yimg.com/8/n/HA07061020/o/701108010144813873435930.jpg The figureshows the graph of the parabola y=2x2 – 12x which cuts the x-axis atthe origin O and at N. ABCD is a rectangle, where A and B are points on thex-axis and C and D are points on the parabola. (a) Find the coordinates of N(b) ... 顯示更多 圖片參考：http://imgcld.yimg.com/8/n/HA07061020/o/701108010144813873435930.jpg The figureshows the graph of the parabola y=2x2 – 12x which cuts the x-axis atthe origin O and at N. ABCD is a rectangle, where A and B are points on thex-axis and C and D are points on the parabola. (a) Find the coordinates of N(b) Let the coordinate of A be (k,0)(i)Write down the coordinates of B and D(ii) Find the area of ABCD in terms of k(iii)If the area of ABCD is 32, find all possible values of kLeave theanswers in surd form if necessary.最佳解答:
The figure shows the graph of the parabola y=2x^2－12x which cuts the x-axis at the origin O and at N. ABCD is a rectangle, where A and B are points on thex-axisand C and D are points on the parabola. (a) Find the coordinates of N Sol 2x^2－12x=0 x(x－6)=0 x=0 or x=6 N(6，0) (b) Letthe coordinate of A be (k，0) (i)Write down thecoordinates of B and D Sol A(k，0) 設B(p，0) k－0=6－p p=6－k B(6－k，0) D(k，2k^2－12k) (ii) Find the area of ABCD in terms of k Sol area of ABCD=(－2k^2+12k)*(6－2k) (iii)If the area of ABCD is32，find all possible values of k Sol (－2k^2+12k)*(6－2k)=32 (－k^2+6k)(3－k)=8 －3k^2+k^3+18k－6k^2=8 k^3－9k^2+18k－8=0 (k^2－7k+4)(k－2)=0 k=(7+√33)/2(不合) or k=(7－√33)/2 or k=2
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