If the quadratic functions F1 (x) = a1x2 + b1x + C1 and F2 (x) = a2x2 + b2x + C2, let F1 (x) + F2 (x) be an increasing function on (- ∞, + ∞) if______ ．

From the meaning of the question, we can get that F1 (x) + F2 (x) can be a linear function, and the coefficient of the linear term is a positive real number, a1 + A2 = 0 and B1 + B2 > 0; so the answer is: a1 + A2 = 0 and B1 + B2 > 0

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1. If the quadratic functions F1 (x) = a1x ^ 2 + b1x + C1 and F2 (x) = a2x ^ 2 + b2x + C2 such that F2 (x) + F1 (x) is listed as an increasing function in (- ∞, + ∞), the condition is
2. If the quadratic function F1 (x) - a1x ^ 2 + b1x + C1, F2 (x) = a2x ^ 2 + b2x + C2, such that F1 (x) + F2 (x) is an increasing function on R, please give the following result If the quadratic function F1 (x) - a1x ^ 2 + b1x + C1, F2 (x) = a2x ^ 2 + b2x + C2, such that F1 (x) + F2 (x) is an increasing function on R, please give a set of F1 (x) =? F2 =?
3. If the quadratic functions f 1 (x) and F 2 (x) satisfy the following conditions: (1) f (x) = f 1 (x) + F 2 (x) monotonically decreases on R; (2) g (x) = f 1 (x) - F 2 (x) pairs (2) For any real number x1, X2 (x1 ≠ x2), if G (x1) + G (x2) / 2 > G (x1 + x2 / 2), then F1 (x) = F2 (x)=
4. As shown in the figure, in the plane rectangular coordinate system xoy, the analytical expression of the parabola is
5. The parabola y = - 1 / 2x square + 3 / 2x + 2 intersects the X axis at two points a and B, and intersects the Y axis at point C (1) ABC is a right triangle (2) : the straight line x = m (0 ∠ m ∠ 4) moves on the line ob, intersects the x-axis at point D, intersects the parabola at point E, intersects BC at point F. when m = what, EF = DF? (3) : after connecting CE and be, "is there a point e to maximize the area of triangle BCE?" if there is a point E, calculate the coordinates of point E and the maximum area of triangle BCE
6. In the plane rectangular coordinate system, the line L and the parabola y ^ 2 = 2x intersect at two points a and B (1) Prove: "if the line L passes through the point t (3,0), then the product of vector OA and vector ob = 3" is a true proposition (2) Write down the inverse proposition of the proposition in (1), judge the truth and explain the reason
7. In the plane rectangular coordinate system, the intersection of the parabola Y1 = x ^ 2-2x + A and the X axis is a, and the intersection of the parabola y2 = x ^ 2 + 2x + 1 + 2a and the X axis is B, and B is symmetric about the Y axis, a is a real number (1) Calculate the value of a and the coordinates of a and B; (2) Do the parabola Y1 and Y2 intersect at a point C on the y-axis? If they intersect at the same point, ask for the area of the largest triangle ABC. If they do not intersect at the same point, please explain the reason
8. Given that the points a (a, Y1), B (2a, Y2), C (3a, Y3) are all on the parabola y = 1 / 2x ^ 2-1 / 2x, find the intersection of the parabola and X-axis? How to find the area of triangle ABC when a = 1? 3. Is there any equation which contains Y1, Y2, Y3 and has nothing to do with a? If so, try to give one and prove it: if not, explain the reason?
9. Given that the points a (a, Y1), B (2a, Y2), C (3a, Y3) are on the parabola y = 5x * x + 12x, find the coordinates of the intersection of the parabola and the X axis (2) When a = 1, find the area of △ ABC
10. The coordinates of the intersection of the line y = x + 2 and the parabola y = x2 + 2x are______ ，______ ．
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12. Given the function y = y1-y2, where Y1 and X are in positive proportion, Y2 and X are in inverse proportion, and when x = 1, y = 1; when x = 3, y = 5
13. If we know that the two tangents of parabola C1: y2 = x + 1 and parabola C2: y2 = - x-a are perpendicular at the intersection, we can find a
14. It is known that line L and parabola C1: y = - X2, C2: y = - x2 + ax are tangent to points a and B respectively, and Given that the line L is tangent to the parabola C1: y = - X2, C2: y = - x2 + ax respectively, and points a, B, "ab" = 3 root sign, 5 divided by 4, find the value of A
15. Given that parabola C1: y = 2x2 and parabola C2 are symmetric with respect to line y = - x, then the Quasilinear equation of C2 is () A. x=18B. x=-18C. x=12D. x=-12
16. Given the image of parabola C1: y = x ^ 2-2x as shown in the figure, fold the image of C1 along the Y axis to get the image of parabola C2 Given the image of parabola C1; y = x ^ 2-2x as shown in the figure, fold the image of C1 along the Y axis to get the image of parabola C2. 1) if the line y = x + B and parabola y = ax ^ 2 + BX + C (a is not equal to 0) have and only have one intersection, the line is said to be tangent to the parabola. If the line y = x + B is tangent to parabola C1, the value of B is calculated 2) When the line y = x + B and the image C1, C2 have two intersections, the value range of B
17. The curve C1: y = x ^ 2yu and C2: y = - (X-2) ^ 2, the line L and C1C2 are tangent, find the equation of the line L. use the derivative function of two curves to find out why it can't be used
18. Given the curve y = - x ^ 3 + 2x, find the linear equation which passes through point B (2,0) and is tangent to curve C? Derivative = -= I set a point (x0, Y0), and then f (x0 + △ x) - f (x0) / △ x, want to find its derivative function = = but it's so strange, is it - △ x ^ 2-3x0 ^ 2-3 △ xX0 + 1, is it my method problem or wrong calculation? = = because I feel that △ x should all be reduced
19. As shown in Figure 11, parabola and straight line y = kx-4k (k)
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