已知二次函数y=-x2+bxc的图像与x轴的交点坐标为(m-2,0),(2m+1,0)80

1、由韦达定理x1 + x2 = -b/a，b = x1 + x2 = m - 2 + 2m + 1 = 3m - 1；x1x2 = -c/a，c = x1x2 = ( m - 2 )( 2m + 1 )；2、抛物线开口向下，y的最大值是顶点；对称轴 x = ( x1 + x2 )/2 = ( 3m - 1 )/2，-2≤ ( 3m - 1 )/2 ≤ 1，-1 ≤ m ≤ 1；①顶点y = b^2/4 - c = 1( 3m - 1 )^2/4 - ( m - 2 )( 2m + 1 ) = 1整理，m^2 + 6m + 5 = 0( m + 1 )( m + 5 ) = 0；m = -1或m = -5；由 ① ，取m = -1。3、代入点A、B坐标，直线AB [x - (-1) ]/[ 2 - (-1) ] = [ y - ( -2m^2 - 3m ) ]/[ ( -2m^2 + 6m ] -( -2m^2 - 3m ) ][ x + 1 ]/3 = [ y + 2m^2 + 3m ) ]/[ 9m ]y + 2m^2 + 3m = 3mx + 3my =3mx - 2m^2交点处，-x^2 + ( 3m - 1 )x - ( m - 2 )( 2m + 1 )= 3mx - 2m^2x^2 + x - 3m - 2 = 0判别式 △ = 1 + 4(3m + 2 ) > 03m + 2 > -1/43m > -9/4m > =3/4m取值范围是m > -3/4 。