"What is the Maximum Area" Quadratic Function PPT Courseware 4

Description

"What is the Maximum Area" Quadratic Function PPT Courseware 4

learning target:

1. Explore the problem of the maximum area of ​​a rectangle and the problem of the maximum light transmission area of ​​a window.

2. Be able to analyze the quadratic function relationship between variables in the problem and solve the maximum (minimum) value problem.

3. Summarize problem-solving strategies and master problem-solving methods.

Self-study guide:

Read pages 67-68 of the textbook and think about the following questions:

1. What are the similar triangles in Figure 2-21? When AB changes, does AD also change? Does the area of ​​the rectangle change?

2. Assume AB=x, then AD=___________. (Expressed by an algebraic expression containing x) How to find the area y?

3. When x changes in Figure 2-22, does y change accordingly? What about the area?

4. Write the relationship between y and x___________. How to find the area?

5. Two questions on page 67 summarize the basic methods for solving such problems.

Self-study test:

In Rt△ MAN, AN=40m, AM=30m, make a rectangle ABCD inside it,

1. There are ____________________ similar triangles in the picture.

2. Assume AB=xm, then AD=____________. (Expressed by an algebraic expression containing

3. Assume AD=xm and the rectangular area is ym², find the maximum area of ​​the rectangle.

When is the largest area?

As shown in the figure, draw a rectangle ABCD inside a right triangle, where AB and AD are on the two right-angled sides respectively.

(1). Suppose one side of the rectangle AB=xm, then how to express the length of side AD?

(2). Assume the area of ​​the rectangle is ym². When x takes what value, what is the maximum value of y?

The idea of ​​"quadratic function application"

Looking back at the process of solving the problem of "maximum profit" in the previous section and "maximum area" in this section, can you summarize the basic ideas for solving such problems? Communicate with peers.

1. Understand the problem;

2. Analyze the variables and constants in the problem and the relationship between them;

3. Express the relationship between them mathematically;

4. Do mathematical solutions;

5. Check the rationality of the test results.

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For more information about the PPT courseware "What is the maximum area of ​​a quadratic function", please click on the ppt label of "What is the maximum area of ​​a quadratic function ppt".

"What is the Maximum Area" Quadratic Function PPT Courseware 5:

"What is the Maximum Area" Quadratic Function PPT Courseware 5 Learning Objectives: 1. Master the problem of the maximum light transmission area of ​​rectangles and windows, and understand the mathematical model thinking and mathematical application value. 2. Learn to analyze and express quadratic relations between variables in practical problems in different contexts.

"What is the maximum area" Quadratic Function PPT Courseware 3:

"What is the Maximum Area" Quadratic Function PPT Courseware 3. Carefully observe the construction model as shown in the figure. Make a rectangle ABCD inside a right triangle, where AB and AD are on the two right-angled sides respectively. (1) Let one side of the rectangle AB=xm So how to express the length of side AD? Analysis..

"What is the Maximum Area" Quadratic Function PPT Courseware 2:

"What is the Maximum Area" Quadratic Function PPT Courseware 2 Teaching Objectives 1. Through review, further master the relevant properties of quadratic functions. 2. Be able to use quadratic function models to solve simple practical problems. Focus: sort out the content learned and construct knowledge that conforms to students’ cognitive structure..

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Update Time: 2024-11-20

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade Mathematics Volume 2 industry PPT template

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