Given the quadratic function y = (x-m) 2 - (x-m), if the vertex coordinates of the quadratic function image is (5 / 2, n), find the value of M, n

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• 1. No matter what the value of M is, the image of quadratic function y = x ^ 2 - (2-m) x + m always passes through the point? Why (1 + x) M = Y-X ^ 2 + 2x find out this step and then how to do it?
• 2. Given the points a (- 1, m), B (- 2, n) on the image of quadratic function y = -- X ^, compare the size of M and n
• 3. Given the points a (- 1, m), B (- 2, n) on the image of quadratic function y = - x?, the size of M and N are compared
• 4. Given that point a (- A & # 178; - 1, m) and point B (- 1, n) are on the image of quadratic function y = x & # 178;, then the size relation of M and N is___ .
• 5. It is known that the quadratic function y = f (x) and G (x) = x ^ 2 have the same image opening size and direction, and the minimum value of y = f (x) at x = m is - 1 If the maximum value of the function y = f (x) on the interval [- 2,1] is 3, find M
• 6. The quadratic function f (x) = x ^ 2 + (m-1) x + 1, if any x belongs to R, f (x) > 0 is constant, the range of M is obtained
• 7. It is known that y = f (x) is a quadratic function and f (- 2 / 3-x) = f (- 2 / 3 + x), which holds for X ∈ R, F (- 2 / 3) = 49, the difference between the two real roots of the equation f (x) is only 7, (1) find the analytic expression of quadratic function, (2) find the maximum value of F (x) in the interval [T, t + 1], T is a random number, not a fixed value There are three cases where t + 1 is on the left, right and middle of the axis of symmetry
• 8. The quadratic function f (x) = ax ^ 2 + (A-1) x + A is known The function g (x) = f (x) + (1 - (A-1) x ^ 2) / X is an increasing function on (2,3). Find the value range of real number a
• 9. The quadratic function f (x) = ax ^ 2 + X is known Given quadratic function f (x) = ax ^ 2 + X (a belongs to R, a ≠ 0) (1) For any x1, X2 ∈ R, compare the size of 1 / 2 * [f (x1) + F (x2)] and f [(x1 + x2) / 2] (2) If x belongs to [0,1], with absolute value f (x) ≤ 1, the value range of a is obtained
• 10. It is known that the quadratic function y = f (x) satisfies f (- 2) = f (0) = 0, and the minimum value of F (x) is - 1 (1) If the function y = f (x), X ∈ R is an odd function, when x > 0, f (x) = f (x), find the analytic expression of the function y = f (x), X ∈ R (2) Let g (x) = f (- x) - t · f (x) + 1. If G (x) is a decreasing function on [- 1,1], the value range of real number T is obtained
• 11. It is known that the image of quadratic function y = x2 + BX + C passes through two points a (n, - 2), B (1, m) on the line y = x-4. (1) find the value of B, C, m, N; (2) find the value of B, C, m, N; (3) find the value of B, C, m, N; (4) find the value of B, C, m, m, N; (4) find the value It is known that the image of quadratic function y = x2 + BX + C passes through two points a (n, - 2), B (1, m) on the line y = x-4 (1) Find the value of B, C, m, n; (2) Judge whether the point C (m, n) is on the image of the quadratic function and explain the reason
• 12. The meaning of algebraic expression According to your life experience, please correct the algebraic formula X / 2 + 3Y
• 13. What are the value ranges of X in the algebraic formula √ x + 1 / X and √ x + 1 / x
• 14. The value range of the letter in the algebraic formula y = x + 1 / 3-2x is____ Square of (- 2 radical 3)=
• 15. Find the value range of the letter X in the algebraic formula [√ (x + 3) + √ (2-x)] / [(x-1) (x + 4)]
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• 17. Use 24 small squares with the side length of 1cm to form a rectangle. How many centimeters is the circumference of the rectangle
• 18. A simple harmonic motion of an object with a period of 4S and an amplitude of 2cm, from t / 8 to t, the distance of the particle motion is 7cm
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