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高考对二次函数的考查主要体现在两个方面:一是对二次函数的图像和性质本身的考查,包括二次函数的单调性、最值、图像的对称性等;二是对二次函数与其他知识交汇问题的考查,包括二次函数与导数、函数零点、不等式等知识的交汇.一、二次函数在给定区间上的最值问题例1已知函数f(x)=-x~2+2ax+1-a在区间[0,1]上的最大值为2,求a的值.解函数f(x)=-x~2+2ax+1-a=-(x-a)~2+a~2-a+1,对称轴方程为x=a.
The examination of the quadratic function of the college entrance examination is mainly reflected in two aspects: First, the quadratic function of the image and the nature of the test, including the monotonic quadratic function, the most value, the symmetry of the image; second is the second Function and other knowledge intersection problem examination, including the intersection of the quadratic function and the derivative, the function zero, inequality, etc. First, the quadratic function in the given interval on the most value problem Example 1 Known function f (x) = - The maximum value of x ~ 2 + 2ax + 1-a in the interval [0,1] is 2. Find the value of a. The solution function f (x) = - x ~ 2 + 2ax + 1-a = - (xa) ~ 2 + a ~ 2-a + 1, the symmetry axis equation is x = a.