"Using Three Ways to Express Quadratic Functions" Quadratic Function PPT Courseware

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"Using Three Ways to Express Quadratic Functions" Quadratic Function PPT Courseware

Do it

The perimeter of the rectangle is known to be 20cm, and its side length is xcm and its area is ycm².

What is the law of y changing with x? Can you express it using function expressions, tables and images?

In the above question, what is the range of values ​​of the independent variable x?

Because x represents the side length of a rectangle with a perimeter of 20cm, x>0,10-x>0. Therefore, the value range of the independent variable x is 0

When x takes on what value, the area of ​​the rectangle is the largest? What is its maximum area?

y=-x²+10x=-(x-5)²+25

∴When X=5, Y maximum=25

That is, when x=5cm, the rectangle has the largest area, and its maximum area=25cm².

When 0

When 5

Based on the above three expressions, answer the following questions:

1. What is the value range of the independent variable x?

∵x represents any number

∴The value range of the independent variable x is: all real numbers

2. What are the symmetry axis and vertex coordinates of the image?

From the vertex expression of the expression and the image, we can see that the symmetry axis of the image is: straight line x=1, and the vertex coordinates are: (1,-1).

3. How to describe the change of y as x changes?

From the tables and images, we can see that y changes as x changes: when x<1, y decreases as x increases; when x>1, y increases as x increases.

Discuss

Expressions are the basis and focus, tables are the key to drawing images, and images are the overall summary and visual expression of functions based on expressions and tables.

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"Using Three Ways to Express Quadratic Functions" Quadratic Function PPT Courseware 4:

"Using Three Ways to Express Quadratic Functions" Quadratic Function PPT Courseware 4 Learning Objectives 1. Experience the process of expressing the quadratic function relationship between variables in three ways, and understand the connections and differences between the three ways. 2. Be able to Analyze and represent quadratic functional relationships between variables,...

"Using Three Ways to Express Quadratic Functions" Quadratic Function PPT Courseware 3:

"Using Three Ways to Express Quadratic Functions" Quadratic Function PPT Courseware 3 Do it. It is known that the perimeter of the rectangle is 20cm and its side length is xcm and its area is ycm. What is the law of y changing as x changes? Can you express it using function expressions, tables and images? ..

"Using Three Ways to Express Quadratic Functions" Quadratic Function PPT Courseware 2:

"Using Three Ways to Express Quadratic Functions" Quadratic Function PPT Courseware 2 Review and Consolidation Leading Questions 1. Definition of quadratic function: y=ax+bx+c (a0) General formula: y=ax+bx+c (a0 ) Vertex formula: y=a(x-m)+n(a0) Two radical formula: y=a(x-x1)(x-x2)..

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Update Time: 2024-11-29

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

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