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

Description

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

learning target:

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 the quadratic function relationship between variables in practical problems under different backgrounds, and use the knowledge of quadratic functions to solve practical problems.

example

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=xcm, then how to express the length of side AD?

(2) Suppose the area of ​​the rectangle is ycm2. When x takes what value, y takes the maximum value. What is the maximum value of y?

Practice in class

1. (2010 Baotou High School Entrance Examination) Cut a 20cm long iron wire into two sections, and use the length of each section of iron wire as the perimeter to make a square. Then the minimum value of the sum of the areas of the two squares is _____cm2 ．

2. (2010·Wuhu High School Entrance Examination) Use a metal material with a length of 20m to make a metal frame as shown in the figure. The lower part is a rectangle and the upper part is an isosceles right triangle. The length of its hypotenuse is 2x m. When the area of ​​the figure enclosed by the metal frame is the largest, what are the lengths of the two adjacent sides of the rectangle in the figure? Find the maximum area of ​​the figure enclosed by the metal frame.

3． (2010 Weifang High School Entrance Examination) The school plans to use floor tiles to lay the ground ABCD of the rectangular square in front of the teaching building. It is known that the length of the rectangular square is 100 meters and the width is 80 meters. The pattern design is as shown in the figure: the four corners of the square are small squares , the shaded parts are four rectangles, the widths of the four rectangles are the side lengths of the small squares, the shaded parts are paved with green floor tiles, and the remaining parts are paved with white floor tiles.

(1) If the area for laying white floor tiles is 5200 square meters, then how many meters are the side lengths of the small squares at the four corners of the rectangular square?

(2) As shown in the figure, the cost of laying white floor tiles is 30 yuan per square meter, and the cost of laying green floor tiles is 20 yuan per square meter. When the side length of the small squares at the four corners of the square is how many meters, the total cost of laying the square floor least? What is the minimum fee?

[Regular method] First convert the actual problem into a mathematical problem, and then express the desired problem using a quadratic function relationship, and then use the vertex coordinate formula or the combination method to find the optimal value. Sometimes the value of the independent variable must be considered Range, find the maximum value based on the image.

Summary of this lesson

The basic idea of ​​​​solving the "maximum area" problem.

1. Read the title and understand the question.

2. Analyze the variables and constants in the problem and the relationships between them.

3. Use quantitative expressions to express the relationship between them.

4. Find the maximum value and minimum value based on the maximum value problem of the quadratic function.

5. Check the rationality and expansion of the test results, etc.

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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 4:

"What is the Maximum Area" Quadratic Function PPT Courseware 4 Learning Objectives: 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 (small) ) value issue. 3. Summary and problem solving..

"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: 2024-10-03

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

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