If the parabola y = - x2 + 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 = - x2 + 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______ ．

From the meaning of the question, M + 1 ＞ 04 (m − 1) & nbsp; 2 + 4 (M + 1) ＞ 0, the solution is: m ＞ - 1, so the answer is: m ＞ - 1

It is known that the vertex of the parabola y = minus one sixth of the square of X + BX + C is p, intersecting with the positive half axis of X axis, two points a (x1,0) and B (x2,0) (x1 < x2), intersecting with y axis
Let m (0, - 2 / 3) be the tangent of the circumscribed circle of the triangle ABC. If am is parallel to BC, the analytic expression of the parabola is obtained

As shown in the figure, if the parabola y = - x2 + 2 (M + 1) x + m + 3 intersects the X axis at two points a and B, and OA: OB = 3:1, then M=______ ．

Let a (3a, 0), B (- A, 0), 2A = 2 (M + 1) 3a · (− a) = − 3

As shown in the figure, the parabola y = 1 / 2x2 + MX + n (n is not equal to 0) intersects the straight line y = x at two points a and B, intersects the Y axis at C, OA = 0

(1) Since the object line y = 1 / 2x2 + MX + n (n is not equal to 0) intersects with the straight line y = x at two points a and B, so X1 and X2 in a (x1, Y1) and B (X2, Y2) are the two roots of the equation x = 1 / 2x2 + MX + N, that is, 1 / 2x2 + (m-1) x + n = 0 / x0d & lt; 1 & gt; two roots