If the ordinate of the lowest point of the parabola y = MX square + 2mx + 2m-1 is zero, then M=

If the ordinate of the lowest point of the parabola y = MX square + 2mx + 2m-1 is zero, then M=

Y = MX square + 2mx + 2m-1 = m (x + 1) ^ 2 + M-1
If the ordinate of the lowest point is zero, then M-1 = 0
m=1

It is known that the parabola y = xsquare-2 (M + 1) x + 2 (m-1),
It is proved that the parabola and X-axis intersect at two points regardless of the sum value of M
If the intersection of the parabola and the x-axis is (3,0), try to find the coordinates of M and Ning Yi point
Let the two intersections of parabola and X-axis be distributed on the left and right sides of (4,0), which is to determine the value range of M

(1) Δ = 4 (M + 1) ^ 2-8 (m-1) = 4m ^ 2 + 12 > 0, so regardless of the sum value of M, the parabola and X-axis intersect at two points (2). Substitute (3,0) into the equation to get m = 1 / 4. Let another point coordinate be (a, 0), then a + 3 = 2 (M + 1) = 2.5, a = - 0.5, coordinate (- 0.5,0) (3) let two points be (a, 0) (B, 0) two intersections