"Application of Quadratic Equations of One Variable" PPT Courseware 4

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"Application of Quadratic Equations of One Variable" PPT Courseware 4

Review and review

We obtain the roots of quadratic equations by completing the square method. This method of solving quadratic equations is called solving by completing the square.

Assistant for solving quadratic equations of one variable using the combination method:

The meaning of square root:

If x2=a, then x=±√a

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: factorize the left side of the equation and combine similar factors 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.

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)

independent work

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 along the directions AC and BC respectively. Their speeds are both 1m/s. .How many seconds later will the area of ​​△PCD be half of the area of ​​Rt△ACB?

Concluding message

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 method of mathematical equations - that is, the idea of ​​equations.

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For more information about the "Applications of Quadratic Equations" PPT courseware, please click on the "Applications of Quadratic Equations ppt" tab.

"Applications of Quadratic Equations of One Variable" PPT courseware 3:

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"Applications of Quadratic Equations of One Variable" PPT courseware 2:

"Applications of Quadratic Equations" PPT Courseware 2 Review and Review 1 The general steps for solving word problems using a series of equations are: 1. Review: Review the meaning of the question: What is known and what is required? What is the relationship between the known and unknown? 2 . Assume: Assume that the unknown number statement must be complete and have the same unit (the same). The unit must be specified...

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Update Time: 2024-07-06

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 1 industry PPT template

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