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

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

Take a closer look at the construction model

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?

Analysis: Assume AD=bm, from the meaning of the question:

ABCD is a rectangle, CD∥AB, where AB=xm, easy to get: x/40=30-b/30

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

Analysis: Because ABCD is a rectangle, the adjacent side AB=xm, (0

AD=b=-3/4X+30

The area of ​​the rectangle y=xb=x(-3/4x+30)

Expand your thinking and discuss

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) If one side of the rectangle AD=xm, how to express the length of side AB?

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

As shown in the figure, draw a rectangle ABCD inside a right triangle, with points A and D on the two right-angled sides, and BC on the hypotenuse.

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

(2) Suppose 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. Use functional models to express the mathematical relationships between variables;

4. Use mathematical methods to solve problems;

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 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 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 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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