Given that the function f (x) = 4x ^ 2-mx + 5 is an increasing function in the interval [- 2, negative infinity), then the value range of M is

Given that the function f (x) = 4x ^ 2-mx + 5 is an increasing function in the interval [- 2, negative infinity), then the value range of M is

Your interval is not right. Is it inverse or positive infinity? Inverse problem is not solved, positive infinity m ＜ - 16

It is known that the image of quadratic function y = AX2 + BX + C intersects with X axis at two different points a and B. point a is on the left side of point B and intersects with y axis at point C. if the sum of areas of △ AOC and △ BOC is 6 and the vertex coordinates of the image of quadratic function are (2, - a), the analytic expression of the quadratic function is obtained

Let a (m, 0), B (4-m, 0). Since point a is on the left side of point B, there is m ＜ 4-m, that is, there is m ＜ 2. The sum of the areas of ∵ AOC and △ BOC is 6, and ∵ MC2 + (4 − M) C2 = 6. The parabolic equation is y = AX2 + BX + 3. ∵ B2A The analytic expression of the function is y = 35x2-125x + 3

It is known that the image of quadratic function y = AX2 + BX + C (a ≠ 0) passes through points a (1,0), B (2,0), C (0, - 2), and the line x = m (M > 2) intersects with X axis at point D (1) (2) there is a point E (point E is in the fourth quadrant) on the straight line x = m (M > 2), so that the triangle with E, D and B as the vertex is similar to the triangle with a, O and C as the vertex, and the coordinates of point e (expressed by the algebraic formula containing m) can be obtained; (3) if (2) is true, is there a point F on the parabola, so that the quadrilateral abef is a parallelogram? If it exists, request the value of M and the area of quadrilateral abef; if not, please explain the reason

(1) According to the title, a + B + C = 04A + 2B + C = 04A + 2B + C = 04A + 2B + C = 0C = -2, a = -1, B = 3, C = -2, and {y = -2 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\it's not easy ）(3) suppose that there is a point F on the parabola such that the quadrilateral abef is a parallelogram, then EF = AB = 1, the abscissa of point F is M-1, when the coordinate of point E1 is (m, 2-m2), the coordinate of point F1 is (m-1, 2-m2), ∵ point F1 is on the parabola image, ∵ 2-m2 = - (m-1) 2 + 3 (m-1) - 2, ∵ 2m2-11m + 14 = 0, ∵ 2m-7) (m-2) = 0, ∵ M = 72, M = 2 (rounding off), ∵ F1 (52) When the coordinates of point E2 are (m, 4-2m), the coordinates of point F2 are (m-1, 4-2m), ∵ point F2 on the parabola image, ∵ 4-2m = - (m-1) 2 + 3 (m-1) - 2, ∵ m2-7m + 10 = 0, ∵ m-2) (m-5) = 0, ∵ M = 2 (rounding off), M = 5, ∵ F2 (4, - 6), ∵ s parallelogram abef = 1 × 6 = 6

What is the C of quadratic function y = AXX + BX + C in this period? Is it the intersection of parabola on Y-axis? For example, C = - 8, then
What is the C of quadratic function y = AXX + BX + C in this period? Is it the intersection of parabola on Y-axis? For example, C = - 8, is it the intersection of parabola on Y-axis?

To be exact:
When x = 0, y = C. that is to say, a quadratic function always intersects the y-axis at the point (0, c), or the ordinate of the intersection of the image of the quadratic function and the y-axis is C