If the parabola y = - X & # 178; + 2 (m-1) x + m + 1 intersects with X axis at two points a and B, and point a is on the positive half axis of X axis and point B is on the negative half axis of X axis, then the value range of M is?

If the parabola y = - X & # 178; + 2 (m-1) x + m + 1 intersects with X axis at two points a and B, and point a is on the positive half axis of X axis and point B is on the negative half axis of X axis, then the value range of M is?

The solution comes from the problem
Equation = - X & # 178; + 2 (m-1) x + m + 1 = 0,
Know Δ > 0 and x1x2 < 0
That is, 4 (m-1) ^ 2-4 (- 1) (M + 1) > 0 and x1x2 = (M + 1) / (- 1) < 0
That is m ^ 2-2m + 1 + m + 1 > 0 and M + 1 > 0
That is, m ^ 2-m + 2 ＞ 0 and m ＞ - 1
That is, (m-1 / 2) ^ 2 + 7 / 4 ＞ 0 and m ＞ - 1
That is, m belongs to R and m ＞ - 1
The solution is m ＞ - 1

Parabola y = - X & # 178; + (m-1) x + m intersects with y axis at point (0,3). (1) find out the value of M and draw this parabola; (2) when x takes what value, y follows X
Increase and decrease?

(1) Take point (0,3) into parabola y = - X & # 178; + (m-1) x + m to get m = 3, take M = 3 into parabola y = - X & # 178; + (m-1) x + m to get y = - X & # 178; + 2x + 3 when y = 0, i.e. 0 = - X & # 178; + 2x + 3 to get x = 3 or x = - 1, i.e. parabola y = - X & # 178; + 2x + 3 passing through point (0,3), (3,0), (- 1,0), i.e. drawing parabola