As shown in the figure, given that the abscissa of the vertex P of the image with quadratic function y = AX2 + BX + C (a ≠ 0) is 4, the X axis of the image intersects point a (m, 0) and point B, and M > 4, then the length of AB is () A. 4+mB. mC. 2m-8D. 8-2m

Because the abscissa of the vertex P of the image of the quadratic function y = AX2 + BX + C (a ≠ 0) is 4, the straight line of the parabola symmetry axis is x = 4, intersecting the X axis at point D, so a and B are symmetrical about the symmetry axis. Because point a (m, 0) and M > 4, that is, ad = M-4, so AB = 2ad = 2 (M-4) = 2m-8, so C
Given the function f (x) = 2x3 + X + SiNx + 1, if f (a) + F (a + 1) > 2, then the value range of real number a is______ .
Let g (x) = f (x) - 1 = 2x3 + X + SiNx. ∵ g (- x) = - G (x), ∵ g (x) is an odd function. ∵ G '(x) = 6x2 + 1 + cosx ≥ 0, ∵ g (x) increases monotonically on R, ∵ f (a) + F (a + 1) > 2,

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1. The image of the quadratic function y = 1 / 2x & # 178; + bx-3 / 2 intersects the x-axis at point a (- 3,0) and point B, with ab as the edge above the x-axis Make a square ABCD, point P is a moving point on the x-axis, connecting DP, passing through point P, make the vertical line of DP intersect with the y-axis at point E. please write the coordinates of point d directly. When point P moves to where on line Ao (point P does not coincide with a, O), the length of line OE has the maximum value, and find out the maximum value
2. Let the quadratic function f (x) satisfy that f (x + 2) = f (2-x) and the sum of the squares of the two real roots of F (x) = 0 be 10. The image passes through (0,3), and the analytic expression of F (x) is obtained
3. If the image of the quadratic function y = - x square + MX-1 has two different intersections with the line segment AB whose two ends are a (0,3) (3,0), the value range of M is obtained
4. It is known that the quadratic function f (x) satisfies f (2) = - 1, f (- 1) = - 1, and the maximum value of F (x) is 8
5. It is known that the coefficient of quadratic term of quadratic function f (x) is a, and f (0) = 3 (1) If the solution set of the inequality f (x) + 2x < 0 is (1,3), find the analytic expression of F (x) (2) Under the condition of (1), if the real number m satisfies f (m) + 2 > 0, the value range of M is obtained
6. The arithmetic sequence and the arithmetic sequence have some similar properties (1) If M + n = P + Q, then a (m) + a (n) = a (P) + a (q) (2) If M + n = 2p, then a (m) + a (n) = 2A (P) I don't understand the problem for a long time. It means that this is the formula of the mean of the equal difference. Ask me to list the formula of the mean of the equal ratio? Seek the power
7. The coefficients a, B and C of quadratic function f (x) = ax ^ 2 + BX + C are not equal to each other, and they are all in - 4, - 3, - 2, - 1,0,1,2,3 (1) The parabola with the opening upward has___________ Article, (2) The parabola passing through the origin has_____________ Article
8. Given a ≠ 0, quadratic function f (x) = ax2-2x-2a, let the solution set of F (x) > 0 be a and B = {x | 1
9. F (x) = (x + 1) / the limit of (x ^ 2 + 1) when x tends to infinity
10. Solving indefinite integral: ∫ DX / [(SiNx) ^ 2cosx]
11. How to find the indefinite integral of ∫ (x ^ 2) DX / (x + 1) (x + 3)? Well, I'm a bit of a nerd, so I'm not very good at it It is better to use the method of ∫ u'v = UV - ∫ UV '
12. What is the detailed solution of definite integral 1 / 1 + X & # DX
13. Finding definite integral ∫ ln [x + √ (X & # 178; + 1)] DX x belongs to [0,2]
14. It is known that the solution set of inequality ax & # 178; + BX + C > 0 about X is α < x < β, where β > α > 0. The solution set of inequality CX & # 178; + BX + a < 0 is obtained Such as the title
15. The function f (x) is an even function on R. when x ≤ 0, f (x) = x & # 179; + 2x & # 178;, then when x ≥ 0, f (x) = ()
16. Use the image of function to find the solution of the following equation x-3x + 2 = 0. You can take pictures or record the answers
17. If the quadratic inequality KX & sup2; - 2x + 6K on X
18. If inequality KX ^ - 2x + 6K
19. Solving the absolute value inequality?
20. Solve the following inequality | 3x | > 1; | X of 2|