Of course, the premise is to have a comprehensive understanding of the solutions of a quadratic equation, and to choose a suitable method in the process of solving the equation, and to solve the size of unknown numbers as soon as possible. This is the most basic content.

Grade 9 Mathematics | Special explanation of the application of quadratic equations + Analysis of six major questions + Special training

The application of quadratic equations mainly learns the practical life problems related to quadratic equations, and focuses on mastering the solutions to typical types of application problems and the steps to solve application problems. Of course, the premise is to have a comprehensive understanding of the solution of a quadratic equation, and to choose a suitable method in the process of solving equation in , and solve the size of unknown numbers as soon as possible. This is the most basic content. For each type of problem-solving method and analysis technique in the application type of quadratic equations, students need to understand the methods used in the analysis process and problem-solving techniques.

Secondly, the main ideas for solving application problems and basic problem-solving steps for quadratic equations are students' main ideas when solving such application problems.

(1) analyze the meaning of the question and find the equality relationship between the unknown number in the question and the product condition of the question;

(2) set the unknown number, and use the algebraic expression of the set unknown number to represent the remaining unknown number;

(3) find the equality relationship and use it to list the equation;

(4) solve the equation to find the value of the unknown number in the question;

(5) check whether the number of answers is in line with the question and answer it. Below, Teacher Tang will give a comprehensive explanation of the six types of questions for the application of quadratic equations of univariate equations, and each type of question is. methods and techniques. All of them are comprehensively analyzed. How to use the methods and remind you of which aspects are all the key points to pay attention to.

, Propagation, cyclic problems and quadratic equations

Summary of methods for questions such as question types: The transmission problem applies the formula a (1+x) n=A, a represents the number of people before the transmission, x represents the number of people per person per round, n represents the number of days or rounds of transmission, and A represents the final total number of people. When we encounter such communication problems, as long as we solve problems according to such formulas, the problem-solving efficiency can be improved.

, Number Problems and Monoral Quadratic Equations

Method Summary: Application questions about numbers can be roughly divided into three categories, namely general number relationship problems, continuous number problems, and number arrangement problems.

①General number relationship problem, the number relationship is relatively simple. Using addition, subtraction, multiplication, division, sum, difference, product, quotient, multiple, remainder, large, small, equal, as well as law, order, etc., the equation can be listed according to the conditions given in the question.

②There are three types of continuous number problems: continuous integers, continuous even numbers, and continuous odd numbers. Mastering their representation is the key to solving such application problems.

③ Number arrangement problem, for example: three digits = the number on the hundred digits × 100 + the number on the ten digits × 10 + the number on the single digits.

, Growth Rate Problem and Monometric Equation

Method Summary: In the growth rate problem, we must understand the meaning of a(1+x)n=b (where a is the original quantity, x is the average growth rate, n is the number of growth times, and b is the quantity to which it has grown). The original quantity reaches a (1+x) after one growth; on this basis, it will grow again, that is, after the second growth, it will reach a (1+x) (1+x) = a(1+x)2; on this basis, it will grow again, that is, after the third growth, it will reach a (1+x) (1+x) (1+x) = a(1+x)3;…; and so on.

Solution to the growth rate problem formula: a (1±x) n=b.

. Profit problem and the quadratic equation

Method summary: Commonly used relationships regarding profit issues are: Profit = selling price - cost, profit = cost × profit rate, profit = (sell price 1 cost) ÷ cost, selling price = cost × (1 + profit rate).

. Area problem and quadratic equation

Method summary: Geometric figures generally find the equal relationship of from the aspect of area (or volume) . The relevant area (or volume) formula:

Solve the area problem of irregular figures. The usual practice is to convert irregular figures into regular figures, find out the relationship between areas before and after the change, and then list the equation to solve them.

, geometric problems and quadratic equations

Method summary: This question relies on the application of the area formula of the trapezoid and the perimeter formula of the trapezoid, and construct a quadratic equation through area and Pythagorean theorem , and at the same time, use a univariate inequality to determine whether the solution of the univariate quadratic equation is in line with the practical significance.

Through the above analysis and method summary of the six types of questions in the learning of application problems of quadratic equations, I believe that everyone has a comprehensive understanding of the application problems of quadratic equations and has a certain understanding of the application of methods. Then, through the special training of application problems of quadratic equations, I believe that these methods can be obtained. Better training, understanding of the method summary and improving the ability to apply from these questions are the core content of everyone's learning.

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at the end, the application type of quadratic equation. It is the key content in the learning process of quadratic equations. For six types of application questions, each type of problem-solving method is something that everyone should focus on. Only by being able to use the methods of each type of question proficiently, the degree of mastery of this type of question can be clarified. The form of expression of each type of question will be different. As the question types change, you must be able to accurately identify which type of application questions you use. Targeted methods are used to train and get the final results. I hope that students can master the characteristics of each type of application questions during the training process to ensure that their accuracy is improved.

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