As shown in the figure, it is known that the image of quadratic function y = x2 + BX + C passes through points (- 1,0), (1, - 2). When y increases with the increase of X, the value range of X is___ ．

As shown in the figure, it is known that the image of quadratic function y = x2 + BX + C passes through points (- 1,0), (1, - 2). When y increases with the increase of X, the value range of X is___ ．

Substituting (- 1,0), (1, - 2) into the quadratic function y = x2 + BX + C, we get 1-B + C = 01 + B + C = - 2, the solution is b = - 1C = - 2, then the analytic expression of the quadratic function is y = x2-x-2. The axis of symmetry of the function is x = 12, so when y increases with the increase of X, the value range of X is x > 12

If the image of quadratic function y = - X & sup2; + 2x + m has no intersection with X, then the value range of M is?

If the image of quadratic function y = - X & sup2; + 2x + m has no intersection with X, then the value range of M is?
△＝4+4m

If the value of quadratic function y = - x ^ 2 + 4x + m is always less than 0, then the value range of M is

If the constant value is less than 0, the maximum value is less than 0
y=-x²+4x-4+4+m
=-(x-2)²+4+m
Maximum m + 4
So m + 4

4X & sup2; - 4x > 15 to find the solution set of inequality

4X & sup2; - 4x ＞ 15. = = = > 4x & sup2; - 4x + 1 ＞ 16. = = = > (2x-1) & sup2; > 16. = = > | 2x-1 ＞ 4. = = = > 2x-1 ＞ 4, or 2x-1 ＜ - 4, = = = = > x ＞ 5 / 2, or X ＜ - 3 / 2.. x ∈ (- ∞, - 3 / 2) ∪ (5 / 2, + ∞)