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依方程的观点,三个不共线的点确定唯一的二次函数 f(x)=ax~2+bx+c,这与“两点确定唯一的直线”类似.二次函数的某些性质,理应能通过它图象上的有关三个点反映出来.例如,由函数的单调性推知,闭区间[m,n]上二次函数的最大值和最小值必属于集合{f(m),f(n),f(b/2a)}.换言之,在解决与二次函数在闭区间[m,n]上的最值有关的问题时,可立足
From the equation point of view, the three non-collinear points determine the unique quadratic function f(x)=ax~2+bx+c, which is similar to the “two points determine the only straight line”. These properties should be reflected by the three related points on the image. For example, it can be inferred from the monotonicity of the function that the maximum and minimum values of the quadratic function in the closed interval [m, n] must belong to the set {f ( m), f(n), f(b/2a)}. In other words, when solving the problem concerning the maximum value of the quadratic function in the closed interval [m,n],