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

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

Review and consolidate, raise questions

1. Definition of quadratic function:

y=ax²+bx+c（a≠0）

General formula: y=ax²+bx+c (a≠0)

Vertex formula: y=a(x-m)²+n（a≠0）

Two radical formula: y=a(x-x1)(x-x2) (a≠0)

Analyze the problem and summarize

Do it

Textbook Page 61: 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 how y changes as x changes?

Can you express it using function expressions, tables and images respectively?

Analysis: One side of the rectangle is xcm, and the other side can be expressed as (10-x)cm. According to the area formula of the rectangle, the area y of the rectangle can be expressed.

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

Please describe how y changes as x changes.

y=-x+10x=-(x-5)²+25

When 0

When 5

Based on the analysis process of the problem, what are the three ways of expressing quadratic functions?

Analytic method—expressing functions using expressions

List method—representing functions in tables

Graphical method—representing functions graphically

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 and image of the expression, it can be seen that the symmetry axis of the image is: straight line x=1; the vertex coordinate is: (1,-1).

y=(x-1)²-1

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

It can be seen from the tables and images that the change of y with the change of x is:

When x<1, y decreases as x increases;

When x>1, y increases as x increases.

Practice in class to consolidate knowledge

1. Make an image of the function y=x²+6x+1 and fill in the blanks based on the image:

When x=-3, the function takes the minimum value -8;

When x≥-3, y increases with the increase of x. (increase, decrease)

2. The vertex coordinates of the function y=-x²+2x+5 are (1,6), and the opening of the image is downward.

When x=1, the function has a maximum (large, small) value of 6.

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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:

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

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Update Time: 2024-09-30

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