Urgently seeking the image of quadratic function y = ax ^ 2 + BX + A ^ 2 + B (a is not equal to 0)

It can be divided into (1) when a > 0 (2) when a

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1. The graph of quadratic function y = AX2 + BX + C is shown in the figure, then the error in the following relation is A.a＜0 B.c＞0 C.b2-4ac＞0 D.a+b+c＞0 The opening direction is downward, the symmetry axis is x = - 1, and the intersection point with y axis is in the positive half axis
2. As shown in the figure, it is a part of the graph of quadratic function & nbsp; y = AX2 + BX + C (a ≠ 0). The following propositions are given: ① a + B + C = 0; ② b > 2A; ③ two of AX2 + BX + C = 0 are - 3 and 1 respectively; ④ a-2b + C > 0. The correct proposition is () A. ①②B. ②③C. ①③D. ①②③④
3. It is known that f (x) is an odd function defined on R, and f (1) = 1. If the image of F (x) is shifted one unit to the right, the image of an even function is obtained, Then f (1) + F (2) + F (3) f (4) + F (2011) is equal to
4. It is known that f (x) is an even function on R, f (0) = 2. If the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. Then the value of F (1) + F (3) + F (5) + F (7) + F (9) is () A. 1B. 0C. -1D. −92
5. It is known that f (x) is an even function on R. if the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. If f (2) = - 1, then f (1) + F (2) + F (3) + +The value of F (2011) is () A. - 1B. 0C. 1D. Not sure
6. It is known that f (x) is an even function on R. if the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. If f (2) = - 1, then f (1) + F (2) + F (3) + +The value of F (2011) is () A. - 1B. 0C. 1D. Not sure
7. How to prove that F1 (x) = f (x) + F (- x) is an even function and F2 (x) = f (x) - f (- x) is an odd function?
8. F1 (x) = f (x) + F (- x) is even function, F2 (x) = f (x) - f (- x) is odd function, right
9. Let a = (cosx, SiNx), B = (cosy, siny), if | √ 2A + B | = √ 3 | - A - √ 2B |, then cos (X-Y)
10. As shown in the figure, in ladder ABCD, ad ‖ BC, ad = 2, BC = 4, point m is the midpoint of AD, and △ MBC is an equilateral triangle (1) Prove: the trapezoid ABCD is isosceles trapezoid; (2) the moving points P and Q move on the line BC and MC respectively, and ∠ MPQ = 60 ° remains unchanged. Let PC = x, MQ = y, find the functional relationship between Y and X; (3) in (2): when the moving points P and Q move to where, the quadrilateral with points P, m and two points in points a, B, C and D as the vertex is a parallelogram? It also points out the number of parallelograms that meet the conditions. ② when y is the minimum, the shape of △ PQC is judged and the reason is given
11. Given that the image of quadratic function y = AX2 + BX + 4 intersects with X axis at a and B, two points intersect with y axis at C angle ACB = angle ABC AB = 5, find the analytic expression of the quadratic function
12. The image of quadratic function y = x ＾ 2 - (a + 2) x + 2A (a > 0) intersects with X-axis at two points a and B, intersects with Y-axis at C, and the area of △ ABC is 3~
13. As shown in the figure, let the image of quadratic function y = ax & # 178; + BX + C intersect at two points AB, and intersect with y axis at point C, if AC = 8, BC = 6, ∠ ACB = 90 °
14. If the vertex of the image of quadratic function f (x) = - x ^ 2 + 4x + C is on the X axis, then the value of C is
15. Given that the image of quadratic function y = ax & # 178; + BX + C passes (1,0), and a > b > C, then the value range of C / A is?
16. If the image of function f (x) and the image of function g (x) = (0.5) ^ X are symmetric with respect to the straight line y = x, then the monotone decreasing interval of F (2x-x ^ 2) is?
17. If the image of F (x) and G (x) = (12) x is symmetric with respect to the line y = x, then the monotone increasing interval of F (4-x2) is______ ．
18. Given that the image of the function f (x) is symmetric with respect to the y-axis, and the interval is in (- ∞, 0), if x = - 1, f (x) has a minimum value of 3, then in the interval (0, + ∞), if x=__ When, F (x) has the most__ The value is__
19. If the image of the function f (x) = (m-1) x2 + 2mx + 3 is symmetric about the Y axis, then the maximum and minimum values of F (x) in the interval [- 2, - 1] are respectively
20. Given that the function f (x) = (AX2 + x) - xlnx increases monotonically on [1, + ∞), then the value range of real number a is______ ．