函数示意图与值域的求法（The function diagram and the method of range）.docVIP

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函数示意图与值域的求法（The function diagram and the method of range）.doc

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函数示意图与值域的求法（The function diagram and the method of range）

函数示意图与值域的求法（The function diagram and the method of range） The image of the two function Y=ax^2+bx+c (a, B, C is a constant, a = 0) I. properties of parabola The 1. parabola is an axisymmetric figure. The axis of symmetry is straight X = -b/2a. The only intersection point of a symmetric axis and a parabola is a parabola P. In particular, when b=0, the symmetry axis of the parabola is the Y axis (i.e., line x=0) The 2. parabola has a vertex P, whose coordinates are P [-b/2a, (4ac-b^2); /4a]. When -b/2a=0, P is on the Y axis; when delta = b^2-4ac=0, P is on the X axis. 3., the two term coefficient a determines the opening direction and size of the parabola. When a 0, the parabola opens upwards; when a is 0, the parabola opens downward. The larger the |a|, the smaller the opening of the parabola. 4., the coefficients B and the two term coefficients a determine the position of the symmetric axis. When a is the same number as B (i.e., AB 0), the symmetry axis is left at the Y axis; When a and B differ (i.e., ab = 0), the symmetry axis is on the right of the Y axis. The 5. constant, C, determines the intersection of the parabola and the Y axis. The parabola corresponds to the Y axis (0, c) 6. the number of intersections between the parabola and the X axis When b^2-4ac = 0, the parabola has 2 intersection points with the X axis. When the delta = b^2-4ac=0, the parabola has 1 intersection points with the X axis. When b^2-4ac = 0, the parabola has no intersection with the X axis. V. two function and two equation of one element In particular, the two function (hereinafter referred to as function) y=ax^2; +bx+c, When y=0, the two function is the unary two equation about X (the following equation), That is, ax^2; +bx+c=0 At this point, there is no intersection point between the function image and the X axis, that is, whether the equation has a real root. The abscissa of the function and the intersection of the X axis is the root of the equation. I. observation By observing the