|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/quadratic-equations-functions-and-transformations/
课程评论：没有评论
课程名称：二次方程、函数与变换 概述：本课程是为年满18岁的成人或学生设计的 comprehensive 课程，旨在深入讲解二次方程、函数和变换。第一部分的第一节课开始于二次方程的介绍及定义，接着学习如何找到给定二次方程的根。我们还将介绍通过“配方”方法解决二次方程，并推导出适用于所有类型二次方程的通用解法。同时，还涉及到当已知根时如何求取相应的二次方程，包括一些通过图形方法解决的实际问题，如根据顶点位置和形状识别二次方程及函数。在第二节课的第一部分，我们学习如何绘制二次函数或方程的图形，步骤包括找到根、y截距和转折点，并使用基本的导数来计算函数的梯度，从而帮助我们找到转折点并绘制所需图形以获得方程的解。 第三节的讲解包括通过平方根法和因式分解法解决二次方程，这些方法将在此节课中得到更详细的阐述，以便于学员的全面理解。同时，课程还将讨论函数的零点和与之相关的实际问题。 在第四节课中，我们将深入探讨二次函数的变换，包括与变换相关的术语，如缩放、平移、拉伸、反射。我们将介绍顶点形式的抛物线函数变换的解释，分析水平与垂直平移之间的区别。最后，我们会总结二次函数变换的规则，并解决与二次方程和函数相关的实际问题。 本课程适合希望掌握二次方程和函数的学员，内容循序渐进，注重理论结合实践，帮助学员在实际应用中灵活运用所学知识。
This is a comprehensive course designed for adult or student not less than 18 years on quadratic equations, functions and transformations. In section one,we begin lecture one by introducing and defining quadratic equations, followed by finding the roots of a given quadratic equation. Also ,included in this first lecture and that leads us to solving quadratic equations using the method of completing the square.We derived the general formula for solving a quadratic equation of all types. This included finding a quadratic equation when its roots are given with examples.some word problems involving quadratic equation and function by graphical method is treated. This includes identification of quadratic equations and functions by shape and position of vertex point. To plot the graph of quadratic function or equation, we begin by finding the roots, y intercept and the turning point.These are covered within the first body of lecture two. Also, basic derivative of gradient of functions is used. This makes it easy to find the turning point and plot the required graph from which the solutions of the equation are obtained.Lecture three of section three includes solving quadratic equation by square root method followed by a method of factorization. These methods are elaborated much more in this lecture unlike introductory lecture one with more examples for total understanding of the course. Zeros of function and word problems leading to quadratic equations are included.Transformation of quadratic functions is, extensively, covered in lecture four of section four. Terminologies associated with transformation that include shrink, shift, stretch, reflection and translation both in horizontal and vertical positions are included in this lecture four. Interpretation of transformation of parabolic function in vertex form, differences between horizontal and vertical translation are treated as well.Finally,we end lecture four by writing a rule for the transformation of quadratic function and solve real life problems involving quadratic equations and functions.
