OSSD课程知识分享之二次函数的概念

　　大家好，今天我们来聊一下OSSD课程中的二次函数的概念。

　　A quadratic function can be written in a number of ways. Each form has different advantages. In all forms, a determines the direction of the opening and the shape.

　　From the standard form, f(x) = ax2+ bx +c, the y-intercept can be identified as c.

　　From the factored form, f(x) = a (x-r)(x-s), the x-intercepts are identified as r and s.

　　From the vertex form, y=a(x-h)2+k, the coordinates of the vertex can be identified as (h,k). If a is positive, the minimum is k. If a is negative, the maximum value is k.

　　二次函数可以通过多种方式书写。每种形式都有不同的优点。通过这些形式，我们可以确定开口的方向和形状。

　　从标准形式 f(x) = ax2+ bx +c，y轴截距可以标识为 c。

　　从因数形式  f(x) = a (x-r)(x-s)，x轴截距标识为 r 和 s。

　　从顶点形式中，可以将顶点的坐标标识为 （h，k）。如果a为正，则最小值为 k。如果a为负，则最大值为 k。  

　　接下来我们看一下二次函数介绍草图的画法：

　　Note that sketches are to be completed by hand. It is intended that all critical points are plotted on the coordinate plane and that the general shape is correct.

　　请注意，草图将由手工完成。它的目的是在所有关键点绘制在坐标平面上，并且一般形状是正确的。

　　Remember:

　　Use a pencil, graph paper, and ruler to complete your graphs. Neatness increases the readability and accuracy of your graph.

　　Linear relations are straight lines. Non-linear relations will require that you plot the graph in a smooth curve.

　　Add labels. Where possible include: equation of the relation, your name, as well as the unit and activity number.

　　•使用铅笔、图形纸和标尺完成图形。图像整洁可提高图形的可读性和准确性。

　　•线性关系是直线。非线性关系需要以平滑曲线绘制图形。

　　•添加标签。如果可能，包括：关系方程、您的姓名以及单位和活动编号。

　　Critical Points / Areas

　　All sketches will start with you finding the critical points of the relation.

　　所有草图都将从查找相关的关键点开始。

　　Intercepts: Locating the x-intercepts and y-intercepts can assure you of some accuracy when sketching the graph of a quadratic or exponential function.

　　End behaviour: The sketch should display typical behaviour of the relation you are working with. In this unit, you are working with quadratics. If a > 0, then both ends of the graph point up. If a < 0, then both ends of the graph point down.

　　Vertex: The vertex of the function is (h, k) when the equation is written in vertex form, y = a(x - h)2 + k.

　　Step Pattern: Quadratic relations have a step pattern that can be used to locate the next point in the graph.

　　Table of Values: A table of values can be generated by substituting known values for the independent variable into the equation of the relation.

　　最后我们看一下二次函数的最大值和最小值：

　　To determine the maximum and minimum value of a quadratic function in the standard form y=ax2+bx+c ,by completing the squares, we rewrite the function in the vertex form y=a(x-h)2+k.

　　The maximum or minimum value of the function is k, when x=h.

　　If a > 0, k is the minimum value of the function.

　　If a < 0, k is the maximum value of the function.

　　如果a>0，那么k便是二次函数的最小值。

　　如果a<0，那么k便是二次函数的最大值。

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