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二次函数类竞赛题是近年来热点问题之一.现将有关竞赛题归类并进行解析.一、求二次函数解析式例1已知二次函数y_1和y_2,当x=a(a>0)时,y_1取得最大值5,且y_2=25;又y_2的最大值为-2,y_1+y_2=x~2+16x+13.求a的值及二次函数y_1、y_2的解析式.解由已知,设y_1=m(x-a)~2+5,贝y_2=x~2+16x+13-m(x-a)~2-5.又当x=a时,y_2=5,即a~2+16a+8=25.解之,得a_1=1,a_2=-17(舍去),故y_2=x~2+16a
Quadratic function race is one of the hot issues in recent years .Classification and analysis of the contest now .A first quadratic function analysisExample 1 known quadratic functions y_1 and y_2, when x = a (a > 0), y_1 gets the maximum value of 5, and y_2 = 25; and the maximum value of y_2 is -2, y_1 + y_2 = x ~ 2 + 16x + 13. Find the value of a and the analysis of quadratic functions y_1, y_2 The solution is known, let y1 = m (xa) ~ 2 +5 and y2 = x ~ 2 + 16x + 13-m (xa) That is a ~ 2 + 16a + 8 = 25. Solution, we have a_1 = 1, a_2 = -17 (rounded off), so y_2 = x ~ 2 + 16a