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1题目(2013年泰州中考题)已知关于z的二次函数y=-x~2+ax(a>0),点A(n,y_1),B(n+1,y_2),C(n+2,y_3)都在这个二次函数的图像上,其中n为正整数。(1)若y_1=y_2,请说明a为奇数;(2)设a=11,求使y_1≤y_2≤y_3成立的所有n的值;(3)对于给定的正实数a,是否存在n,使△ABC是以AC为底边的等腰三角形?如果存在,求n的值(用含a的代数式表示);如果不存在,请说明理由。
1 Question (2013 Taizhou senior high school entrance examination questions) Known about the quadratic function of z y = -x ~ 2 + ax (a> 0), points A (n, y_1), B (n +1, y_2), C n + 2, y_3) are on the image of this quadratic function, where n is a positive integer. (1) Let y be an odd number if y_1 = y_2; (2) Let a = 11, find all the values of n for which y_1≤y_2≤y_3; (3) For a given positive real number a, , So △ ABC is the basis of the isosceles triangle AC? If so, find the value of n (with algebraic representation); If not, please explain the reasons.