7. Given the quadratic function f (x) = AX2 + BX + C, G (x) = λ ax + B (λ≥ 1), when | x | ≤ 1, | f (x) | ≤ 1. (1) it is proved that | a | ≤ 2 (2) Let f (0), f (1), f (- 1) denote g (1), G (- 1) (3) When | x | ≤ 1, it is proved that | g (x) | ≤ 2 λ

RELATED INFORMATIONS

• 1. Given the quadratic function f (x) = AX2 + BX + C (C ≠ 0) (1) if A.B.C and f (1) = 0, it is proved that the image of F (x) has two intersections with the X axis; (2) if Changshu x1 If x 2 ∈ R, and x 1, x 2, f (x 1) ≠ f (x 2), we prove that the equation f (x) = 1 / 2 [f (x 1) + F (x 2)] must have a root belonging to (x 1, x 2)
• 2. It is known that the quadratic function f (x) = AX2 + BX + C (a > 0) has two different common points with the X axis If f (c) = 0 and 0 < x < C, f (x) > 0 1) Compare 1 / a with C 2) Proof - 2 < B < 1
• 3. Quadratic function, f (x) = AX2 + BX + C, f F (x) = AX2 + BX + C, f (x) = f (2-x), f (0) = 3, f (1) = 2.1. Find the analytic formula of function. 2. F (x) belongs to the maximum value of [- 1,2] in X
• 4. Given the quadratic function f (x) = AX2 + BX + C, f (2) = 0, f (- 5) = 0, f (0) = 1, find the quadratic function
• 5. If the quadratic function f (x) = AX2 + BX + C, if f (0) = 0 and f (x + 1) = f (x) + X + 1, then f (x)=
• 6. It is known that the quadratic function f (x) = ax ^ 2 + BX satisfies f (2) = 0 and the equation f (x) = x has equal roots
• 7. It is known that the quadratic function f (x) = ax ^ 2 + BX (AB ∈ R, a ≠ 0) satisfies f (- x + 5) = f (x-3) and the equation f (x) = x has equal roots; It is known that the quadratic function f (x) = ax ^ 2 + BX (AB ∈ R, a ≠ 0) satisfies f (- x + 5) = f (x-3) and the equation f (x) = x has equal roots. (1) find the analytic expression of F (x); (2) whether there are real numbers m, n (m < n), so that the domain of definition and value of F (x) are [M, n] and [3M, 3N]? If there are, find the value of M, N; if not, explain the reason
• 8. It is known that the quadratic function f (x) = ax + BX (a, B are familiar, and a ≠ 0) satisfies the following conditions: F (- x + 5) = f (x-3), and the equation f (x) = x has equal roots (1) The expression of finding f (x) (2) whether there is a teacher's uncle m, n (m) or not
• 9. It is known that f (x) is an odd function defined on R. when x ≥ 0, f (x) = x2-2x, then the expression of F (x) on R is () A. y=x（x-2）B. y=x（|x|-1）C. y=|x|（x-2）D. y=x（|x|-2）
• 10. The problem of derivative in second grade mathematics Find the tangent equation of the curve y = SiNx at point a (6 / 6 π, 2 parts only 1)? 2. Find the tangent equation of the square of the parabola y = x parallel to the line 2x-y = 0? 3. Find the tangent equation of the point (0,0) and the square of the curve y = x? 4. Find the tangent equation of the point (1, - 1) on the curve y = XD 3 power - 2x? To write the process, thank you
• 11. It is known that the derivative f '(x) ≤ f (x) B of quadratic function f (x) = AX2 + BX + C belongs to R. it is proved that f (x) is less than or equal to (x + C) ^ 2 when x ≥ 0
• 12. If f (x) = AX2 + BX (a ≠ 0) satisfies 1 ≤ f (- 1) ≤ 2, 2 ≤ f (1) ≤ 5, then the value range of F (- 3) is______ ．
• 13. If f (x) = AX2 + BX, and 1 ≤ f (1) ≤ 2,2 ≤ f (1) ≤ 4, find the range of F (2)
• 14. Let f (x) = alnx-1 / 2x ^ 2 + BX find the solution set of the inequality f (x) > F (1)
• 15. Let f (x) = alnx − 12x2 + BX. (1) when a = 3, B = 12, find the maximum value of F (x); (2) find the solution set of the inequality f '(x) > F (1)
• 16. The function f (x) = alnx-bx ^ 2 (x ≥ 0) when B = 0, if the inequality f (x) ≥ m + X holds for all a ∈ [0,3 / 2], X ∈ (1, e ^ 2), find the range of M
• 17. What is the domain of (1-e ^ x) under the function f (x) = 1 / radical
• 18. What is the domain of 1-e ^ x under the function f (x) = 1 / radical
• 19. Function y = - x2-2ax (0
• 20. If the maximum value of function f (x) = x & sup2; + 2aX + 1 on [0,1] is f (1), then what is the value range of a