"Application of Quadratic Equations of One Variable" PPT Courseware 2 of Quadratic Equations of One Variable

Description

"Application of Quadratic Equations of One Variable" PPT Courseware 2 of Quadratic Equations of One Variable

We obtain the roots of quadratic equations by arranging them into perfect squares. This method of solving quadratic equations is called the arranging method.

Perfectly square method: The formula a2±2ab+b2 is called a perfectly square method, and a2±2ab+b2 = (a±b)2.

Steps to solve quadratic equations of one variable using the formula method:

1. Transform to 1: Change the coefficient of the quadratic term to 1 (divide both sides of the equation by the coefficient of the quadratic term);

2. Move the term: Move the constant term to the right side of the equation;

3. Recipe: Add half the square of the absolute value of the coefficient of the linear term to both sides of the equation;

4. Deformation: formula on the left side of the equation, merge similar terms on the right side;

5. Square root: According to the meaning of square root, the square root of both sides of the equation;

6. Solve: Solve linear equations of one variable;

7. Definite solution: Write the solution of the original equation.

When one side of a quadratic equation is 0 and the other side is easily decomposed into the product of two linear factors, we can solve it by factoring. This method of solving a quadratic equation by factoring is called is the factoring method.

1. The conditions for using the decomposition factor method are: the left side of the equation is easy to decompose, and the right side is equal to zero;

2. The key is to master the knowledge of factorization;

3. The theoretical basis is "If the product of two factors is equal to zero, then at least one factor is equal to zero."

Example 1 As shown in the figure, a naval base is located at A, with a target B 200 nautical miles due south of it, and an important target C 200 nautical miles due east of B. The small island D is located at the midpoint of AC, and there is an Supply dock; small island F is located on BC and just south of small island D. A warship sets off from A and cruises at a constant speed from B to C. A supply ship starts from D at the same time and cruises in a straight line south-west direction. Sailing to deliver a batch of items to the warship.

(1). How many nautical miles are there between small island D and small island F?

(2). It is known that the speed of the warship is twice that of the supply ship. The warship meets the supply ship at E on the way from B to C. How many nautical miles has the supply ship sailed when it met? (The result is accurate to 0.1 nautical miles)

2. In the residential design of Green Garden Community, a rectangular green space with an area of ​​900 square meters is planned to be opened between every two buildings, and the length is 10 meters longer than the width. So what are the length and width of the green space?

1. There is such an ancient Arabic arithmetic problem: there are two sums of money, one is more and one is less, the sum is equal to 20, and the product is equal to 96. The larger sum is promised to Said, so how much money does Said get?

2. As shown in the figure, in Rt△ABC, ∠C=90°, points P and Q start from two points A and B at the same time, and move toward point C at a constant speed in the direction of AC and BC respectively (until point C). The speeds are all 1m/s. After how many seconds, the area of ​​△PCQ will be half of the area of ​​Rt△ACB?

The quadratic equation is also an effective mathematical model to describe the real world.

Using the method of formulating equations to explain or solve some phenomena or problems in life is an important mathematical method - that is, the idea of ​​equations.

Keywords: quadratic equations teaching courseware, application of quadratic equations teaching courseware, Beijing Normal University edition ninth grade mathematics volume 1 PPT courseware, ninth grade mathematics slide courseware download, quadratic equations PPT courseware download, application of quadratic equations PPT courseware download, .ppt format

For more information about the PPT courseware "Quadratic Equations of One Variable and Application of Quadratic Equations of One Variable", please click the "Quadratic Equations of One Variable Equation ppt Application of Quadratic Equations of One Variable" ppt tag.

"Application of quadratic equations of one variable" PPT courseware of quadratic equations of one variable:

"Application of Quadratic Equations" Quadratic Equations PPT Courseware 1. Area Problem (1) As shown in the figure, three ditches are dug on a rectangular farmland with a length of 92m and a width of 60m. The widths of the ditches are all equal. The ditches divide the farmland into areas. Each is 6 rectangular blocks of 885m2, and the water channel should...

File Info

Update Time: 2024-09-12

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade First Volume Mathematics industry PPT template

Preview