Question

因式分解的数学题

把下列二次三项式写成a(x+m)^2+n的形式
1.x-56+2x^2
2.-3x^2+2x+56
求下列二次三项式的最大值或最小值
1.-6-6x+2x^2
2.-3x^2+2x+5

Answer 1

把下列二次三项式写成a(x+m)^2+n的形式
1.x-56+2x²
=2(x²+x/2)-56
=2(x²+x/2+1/16-1/16)-56
=2(x²+x/2+1/16)-1/8-56
=2(x+1/4)²-449/56

2.-3x^2+2x+56
=-3(x²-2x/3)+56
=-3(x²-2x/3+1/9-1/9)+56
=-3(x²-2x/3+1/9)+1/3+56
=-3(x²-1/3)²+169/3

求下列二次三项式的最大值或最小值
1.-6-6x+2x^2
=2(x²-3x+9/4-9/4)-6
=2(x²-3x+9/4)-9/2-6
=2(x-3/2)²-21/2
所以最小值=21/2

2.-3x^2+2x+5
=-3(x²-2x/3+1/9-1/9)+5
=-3(x²-2x/3+1/9)+1/3+5
=-3(x²-1/3)²+16/3
所以最大值=16/3

Answer 2

把下列二次三项式写成a(x+m)^2+n的形式
1.x-56+2x^2
=2(x^2+x/2+1/16)-1/8-56
=2(x+1/4)^2-449/8

2.-3x^2+2x+56
=-3(x^2-2x/3+1/9)+1/3+56
=-3(x-1/3)^2+169/3

求下列二次三项式的最大值或最小值
1.-6-6x+2x^2
=2(x^2-3x+9/4)-9/2-6
=2(x-3/2)^2-21/2
所以,当x=3/2时,原式有最小值是-21/2

2.-3x^2+2x+5
=-3(x^2-2x/3+1/9)+1/3+5
=-3(x-1/3)^2+16/3
所以,当x=1/3时,原式有最大值是16/3

Answer 3

1.x-56+2x^2
=2(x^2+x/2+1/16)-1/8-56
=2(x+1/4)^2-449/8

2.-3x^2+2x+56
=-3(x^2-2x/3+1/9)+1/3+56
=-3(x-1/3)^2+169/3

1.-6-6x+2x^2
=2(x^2-3x+9/4)-9/2-6
=2(x-3/2)^2-21/2
所以,当x=3/2时,原式有最小值是-21/2

2.-3x^2+2x+5
=-3(x^2-2x/3+1/9)+1/3+5
=-3(x-1/3)^2+16/3
所以,当x=1/3时,原式有最大值是16/3