(urgent! Just finished! Quadratic function f (x) = ax ^ 2 + BX + C (a)

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a

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1. The increase and decrease of quadratic function f (x) = AX2 + BX + C (a < 0) in the interval [- B2A, + ∞) is judged and proved according to the definition
2. It is known that the quadratic function f (x) = AX2 + BX + C satisfies a > b > C, f (1) = 0. The function g (x) = f (x) + BX (1) proves that the function y = g (x) must have two different zeros (2) Let the two zeros of function y = g (x) be x1, X2, and find the absolute value range of x1-x2
3. It is known that the quadratic function f (x) = ax & # 178; + BX + 1 and G (x) = (BX-1) / (A & # 178; X + 2b). When B = 2A, ask if there is a value of x such that any real number a satisfying - 1 ≤ a ≤ 1 and a ≠ 0 holds the inequality f (x) < 4? And explain the reason
4. Given the quadratic function f (x) = AX2 + BX + C, if f (x) + F (x + 1) = 2x2-2x + 13 (1), find the analytic expression of function f (x); (2) draw the image of the function; (3) find the maximum value of function f (x) when x ∈ [T, 5]
5. Given the function y = ax & # 178; + BX + C, if AC < 0, then the number of zeros of function f (x) is
6. If the zeros of the function f (x) = xsquare-b are 2 and 3, try to find the zeros of the function g (x) = bsquare-ax-1
7. If the two zeros of the function f (x) = xsquare - ax-b are 2 and 3, find loga25 + B2
8. Let f (x) = the square of AX + BX + C (a > 0) and f (1) = A / 2 (1)) prove that the function has two zeros
9. If the image of function y = A-X / x-a-1 is symmetric with respect to point (4, - 1), what is the value of real number a?
10. If the function f (x) has f (a + x) = - f (A-X) for all real numbers in the domain of definition, then the image f (x) of the function is a centrosymmetric graph whose center of symmetry is
11. It is known that a, B and C are positive integers, and the quadratic function y = AXX + BX + C. when x is greater than or equal to - 2 and less than or equal to 1, y is larger If y is greater than or equal to - 1 and less than or equal to 7, find the analytic expression of quadratic function
12. What is the condition that the quadratic function y = AXX + BX + C (a is not equal to 0) is always negative "AXX" is a times the square of X
13. Given that the image of quadratic function y = AX2 + BX (a is not equal to 0) of X passes through a (- 1,3), then AB has the maximum value of
14. The image of quadratic function y = ax + BX + C intersects with X axis at points a (- 8,0), B (2,0), and intersects with y axis at point C, ∠ ACB = 90 degree. (1) find the analytic expression of quadratic function. (2) find the vertex coordinates of image of quadratic function
15. Given the function f (x) = - e ^ x, G (x) = LNX, e is the base of natural logarithm
16. If a line y = ex + B (E is the base of natural logarithm) and two functions f (x) = ex, G (x) = LNX have at most one common point, then the value range of real number B is______ ．
17. It is known that the function f (x) = ln (ex + a) (a is a constant) is an odd function on the real number set R, and the function g (x) = λ f (x) + SiNx (λ≤ - 1) is a decreasing function on the interval [- 1,1]; (1) find the value of a; (2) if G (x) ≤ T2 - λ T + 1 is constant on X ∈ [- 1,1], find the value range of T
18. If the function f (x) 4x ^ 2-mx + 5 is an increasing function on the interval [- 2, + ∞), then f (1) has a range of values
19. Given that the function f (x) = 4x ^ 2-mx + 5 is an increasing function in the interval [- 2, negative infinity), then the value range of F (1) is It's on [- 2, positive infinity)
20. 2. Given that the function f (x) = 4x ^ 2-mx + 5 is an increasing function in the interval [- 2, positive infinity), then the value range of F (1) is a, ≥ 25B, = 25C, ≤ 25d, I don't understand why x = - B / 2A ≤ - 2, that is, M / 8 ≤ - 2, m ≤ - 16 Why is x = - B / 2A greater than or equal to - 2?