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数形结合是数学学习中常用的方法之一,这种方法在函数一节应用尤为突出.二次函数中利用图象判别系数a、b、c及其代数式的符号已成为热门考点.二次项的系数a的符号可以根据图象的开口方向来判别;b的符号可以根据对称轴的位置确定;c的符号可以根据图象与y轴的交点位置确定;b~2-4ac的符号可以根据图象与x轴的交点个数确定;a、b、c的代数式符号可以根据某特殊点的函数值确定;下面用几个具体的例子加以说明.
The combination of number and shape is one of the commonly used methods in mathematics learning, and this method is especially used in the section of the function. The symbol of the discriminant coefficients a, b, c and its algebraic formula in the quadratic function has become a hot spot. The sign of the coefficient a of the second term can be discriminated according to the direction of the opening of the image; the sign of b can be determined according to the position of the symmetry axis; the sign of c can be determined according to the position of the intersection of the image and the y-axis; The number of intersection points of the image and the x-axis can be determined. The algebraic signs of a, b, and c can be determined according to the function values of a particular point. A few specific examples are given below.