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历届中考的热点之一,就是运用二次函数解决数学问题或实际问题,此类题目经常需要用二次函数表达其中的变量关系,而求出二次函数的解析式是解题的关键。求二次函数解析式的方法有定义法、平移法、三点法、交点法、顶点法、对称法、旋转法、参数法、等量法等。 相似文献
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求一元二次函数解析式的问题是一个教学重点和难点。一元二次函数的解析式的形式有三类:一般式、两根式、顶点式(交点式)。本文对此进行了一些探析。 相似文献
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作为贯穿初、高中数学课程的一个很重要的知识点,二次函数在解决代数问题和几何解析问题中都起到了很大的作用,被引用的机会很多。此外,二次函数可以作为各种数学思想的载体,能够将不等式、数列、基本函数以及导数等基础部分的内容更加充分的展现出来。由于其在高中数学学习中应用更加广泛和灵活,因此在高中数学中,二次函数扮演者非常重要的角色。本文通过对二次函数的理解及应用,对二次函数在高中数学中的应用提出一些见解。 相似文献
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对称性是函数的一个重要性质，利用函数的对称性可进行函数的最值推导、取值范围的推导，单调区间的确定和解析式的确定。同时还有函数图形对称性的证明，这些都是中学数学的重要内容。都有待我们去深入探究。本文利用二次函数的对称性和函数奇偶性的对称性进行推导，并试图进行函数图象的对称性证明。 相似文献
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高中数学的函数部分是学生学习的一个难点,概念部分有函数的定义,反函数,定义域,值域及解析式。性质部分有单调性,奇偶性及周期性。学生学习过的常见的初等函数有一次函数,二次函数。反比例函数。指数函数,对数函数。正弦函数,余弦函数,正切函数等。事实上。我们在学习的过程中往往遇到形如f（x）=x＋a-x的函数,因为利用它可以考查不等武、最值、函数的单调性、函数的值域等问题。因此也是高考中的热点和难点,颇受命题者的青睐。 相似文献
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函数是中学数学中最重要的概念之一,在初中阶段,一次函数和二次函数是讨论的重点,而二次函数是函数知识的核心内容.在近几年本市中考的压轴题都是出在二次函数中,而在二次函数的解题中,最值问题往往是考生最头疼的.文章就二次函数v=ax2+bx+c(a≠0)的最值问题,分二次函数在给定范围内的最值问题、含字母系数的二次函数的最值问题以及函数最值的应用三类进行剖析. 相似文献
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三角函数与二次函数作为高中数学教学的难点,学生在掌握的过程中本身就会存在难点,将二者整合在一起,对于学生而言又增加了一层难度。本文通过对具体例题的解析,对二次函数和三角函数整合试题的解题方法和步骤进行了详细的分析,希望同学通过对例题解决方法的分析和掌握,对于以后考试中解决此类难题举一反三,触类旁通。 相似文献
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二次函数既可以与代数知识相结合,也可以与几何知识相结合.中考主要考查学生对二次函数的概念、图象、性质及应用的掌握情况以及学生的综合分析问题、解决问题的能力.本文以具体实例分析二次函数中考常考考点及相关解题策略. 相似文献
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变形技巧在数学解题中是很常用的方法,数学解题中,为了完成论证,求值、化简等的任务,需要对一些式子进行恒等变形。一般情况下,一个式子往往有多种变形形式,因题而异,技巧性非常强。本文主要介绍了在初高中数学中的三角函数、因式分解、不等式、一元二次方程等的变形应用。掌握好并灵活运用好变形技巧,可以化复杂为简单,提高解题效率。 相似文献
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在学习中,我们常常会遇到解方程及不等式问题,按常规方法很难分析得出结果,但是利用二次函数思想经过分析,问题就可以迎刃而解了。 相似文献
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In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated. First of all, by using integral-type error function and twice zeroing neural network (or termed, Zhang neural network) formula, as the preliminaries and bases of future problems solving, two continuous-time advanced zeroing neural network models are presented for solving continuous time-variant equation systems. Secondly, a one-step-ahead numerical differentiation rule termed 5-instant discretization formula is presented for the first-order derivative approximation with higher computational precision. By exploiting the presented 5-instant discretization formula to discretize the continuous-time advanced zeroing neural network models, two novel discrete-time advanced zeroing neural network models are proposed. Theoretical analyses on the convergence and precision of the discrete-time advanced zeroing neural network models are proposed. In addition, in the presence of disturbance, the proposed discrete-time advanced zeroing neural network models still possess excellent performance. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed discrete-time advanced zeroing neural network models for solving the future equation systems. 相似文献
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《Journal of The Franklin Institute》2023,360(2):1344-1377
A novel finite-time complex-valued zeroing neural network (FTCVZNN) for solving time-varying Sylvester equation is proposed and investigated. Asymptotic stability analysis of this network is examined with any general activation function satisfying a condition or with an odd monotonically increasing activation function. So far, finite-time model studies have been investigated for the upper bound time of convergence using a linear activation function with design formula for the derivative of the error or with variations of sign-bi-power activation functions to zeroing neural networks. A function adaptive coefficient for sign-bi-power activation function (FA-CSBP) is introduced and examined for faster convergence. An upper bound on convergence time is derived with the two components in the function adaptive coefficients of sign-bi-power activation function. Numerical simulation results demonstrate that the FTCVZNN with function adaptive coefficient for sign-bi-power activation function is faster than applying a sign-bi-power activation function to the zeroing neural network (ZNN) and the other finite-time complex-valued models for the selected example problems. 相似文献
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伊犁新垦区土壤全盐量和电导率定量关系探讨 总被引：3，自引：0，他引：3
土壤含盐量和电导率是调查评价土壤盐渍化程度的两种指标,进行两者关系的定量探讨是解决土壤盐渍化快速诊断问题的前提。本文以伊犁新垦区为例,采用传统的一次函数、二次函数和分段函数等对土壤含盐量和电导率关系进行回归拟合,同时应用土地利用类型、植被类型和土壤类型等环境因子作为辅助数据对两者进行分区线性拟合,并分析比较两种方法的优劣。结果表明,随着全盐量的增加,土壤全盐量和电导率呈现一定的非线性关系,以土壤全盐量为阈值的分段函数拟合效果优于一次函数和二次函数,其RMSE小于后两者;以土地利用类型作为辅助数据进行的分组拟合结果优于植被类型和土壤类型的效果,也略优于分段函数的拟合精度。该方法在宏观尺度上为快速、精确获取土壤盐分状况提供帮助。 相似文献
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In this paper, the quadratic minimax optimal control of linear system with input-dependent uncertainty is studied. We show that it admits a unique solution and can be approximated by a sequence of finite-dimensional minimax optimal parameter selection problems. These finite-dimensional minimax optimal parameter selection problems are further reduced to scalar optimization problems which also admit unique solutions. Thus, the original minimax optimal control problem is solved via solving a sequence of simple scalar optimization problems. Numerical experiments are presented to illustrate the developed method. 相似文献
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结合模松弛SQP算法和强次可行方向算法思想,给出了初始点任意选取的新的拟强次可行方向算法。每步迭代,只需求解一个总有最优解的二次规划子问题来产生主搜索方向,引入一种新的非单调曲线搜索来产生步长,在较弱的条件下,可以得到算法的全局收敛性。 相似文献
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《Journal of The Franklin Institute》2022,359(18):10907-10930
Zhang neural network (ZNN) is widely applied to solving time-dependent problems. For the sake of the implementation on the digital hardware platform, ZNN models need to be discretized. In this paper, as a further study of Zhang et al. discretization (ZeaD) formulas, a novel general 9-instant ZeaD formula is presented, and clear constraints are firstly given with proof. To evaluate the presented 9-instant ZeaD formula, three continuous-time models for time-dependent matrix inversion and pseudoinversion are presented with the help of Getz-Marsden dynamic system (GMDS) and ZNN. Then the corresponding discrete-time models are obtained by using the 9-instant ZeaD formula. According to the comparison experiments, the 9-instant ZeaD formula is substantiated to be effective and consistent with the theory. Furthermore, the problem of mobile angle-of-arrival (AoA) localization is investigated as a more specific and practical problem. In order to overcome the singularity problem of the tangent function in the representation of the AoA localization system, a new representation with sine and cosine functions is presented. Similarly, the continuous-time model is derived and discretized. Through comparison experiments, the discrete-time model obtained by the 9-instant ZeaD formula achieves desirable results, which further show the efficacy of the 9-instant ZeaD formula. 相似文献
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In this paper, a composite Chebyshev finite difference method for solving linear quadratic optimal control problems with inequality constraints on state and control variables is introduced. This method is an extension of Chebyshev finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well known Chebyshev–Gauss–Lobatto nodes. The excellent properties of hybrid functions are used to convert optimal control problem into a mathematical programming problem whose solution is much more easier than the original one. Various types of optimal control problems are investigated to demonstrate the effectiveness of the proposed approximation scheme. The method is simple, easy to implement and provides very accurate results. 相似文献
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《Research Policy》2022,51(3):104453
In an era of rapid technological advances, individuals have access to a plethora of open and closed forms of problem solving. We introduce and test a framework that compares different forms of problem solving and determines how individuals make choices among them. Our analyses of 4,556 problems solved by 398 individuals reveal that high problem complexity and strong implicit social norms of open exchange increase the probability that individuals will seek external solutions rather than solve the problems themselves. Our analysis also shows that they prefer individual experts (contacted directly or via open call) over aggregated crowd knowledge. We also find that strong implicit social norms of open exchange weakened the positive impact of complexity on the probability of solving problems externally. Interestingly, this effect is more subtle when the use of aggregated crowds is compared with individual experts: while strong implicit social norms strengthen the positive impact of problem complexity when experts are contacted directly, they otherwise weaken the use of open call experts. We discuss and examine the nuanced effects between problem complexity and social norms of open exchange. The study contributes to a stream of the open innovation literature that uses a problem solving perspective to better understand under what circumstances certain forms of problem solving are utilized, and it then combines it with a novel empirical setting based on real-life experimental data. 相似文献