"Getting to Know Parabolas" Quadratic Function PPT Courseware

Description

"Getting to Know Parabolas" Quadratic Function PPT Courseware

(1). The status and role of teaching materials

The content of this section is the further function knowledge that students will learn after learning direct proportional functions, linear functions and inverse proportional functions. It is an important link in the spiral development of function knowledge. The quadratic function curve-parabola is also one of the most familiar curves for people. The water flow of fountains and the throwing of javelins all form parabolic paths. At the same time, parabolic shapes are also widely used in architecture, such as parabolic arch bridges, parabolic tunnels, etc. This lesson studies the simplest quadratic function y=±x2 Image is an important link in the process of students learning function knowledge. It is not only a continuation of the knowledge learned previously, but also the basis for exploring the images and properties of the other two functions, and serves as a link between the past and the next.

1. Knowledge and Skills Objectives

(1) Be able to use the point drawing method to draw an image of the function y=x2, and be able to recognize and understand the properties of the quadratic function y=x2 based on the image.

(2) Guess and be able to draw the image of y=-x2, and compare its similarities and differences with the image of y=x2.

2. Process and method objectives

(1) Experience the process of exploring the methods and properties of the graph of the quadratic function y=x2, and gain experience in using images to study the properties of functions.

(2) From the image and properties of the function y=x2, learn the image and properties of y=-x2 comparatively, and compare their similarities and differences, cultivate students' analogical learning ability and develop students' ability to seek common ground and seek differences. thinking.

Teaching analysis

In view of the characteristics of this lesson, the teaching method of "creating situations-drawing and exploring-summarizing-knowledge application" is adopted as the main line.

Put the focus of teaching on how to promote students' "learning", and guide students to adopt diversified learning methods such as observation, experimentation, independent exploration, group activities, collective communication, etc. In the teaching process, we always adhere to the principle of students as the main body and teachers as the leader. The policy integrates inquiry knowledge and ability cultivation, so that students not only learn the methods of scientific inquiry, but also experience the joys and sorrows of inquiry and appreciate the joy of success.

Create situations and ask questions

1. What functions have we already learned? What is the general procedure for studying function problems?

2. What are the graphs of linear functions and inverse proportional functions?

Design intention: Let students review the function types, images and general ideas for studying function problems they have learned, so that students can use analogy methods to study related problems of quadratic functions.

Cooperate and exchange, explore new knowledge

1. Get to know the parabola

Design Intention: The images obtained by students’ lists, drawing points, and connecting lines are easy to draw as polyline graphics, so it is difficult to understand the essence of why smooth curves are used to connect the points. Use the geometric sketchpad to use lists and associate them with images. The method is to increase the number of points that satisfy the function within the unit interval, so that the true appearance of the image can be seen.

Question: Through the analysis just now, do you think that when drawing the image of y=x2:

(1) What issues should be paid attention to when selecting list values?

(2) What kind of lines are used to connect points?

2. Explore the properties of parabola y=x2

Discuss: Please observe the image of y=x2, first discuss what aspects of properties we need to explore, and then discuss in groups.

Teacher-student behavior: After students discuss and communicate, ask the student representatives of each group to express their observations one by one. In this process, the teacher cannot be the judge, but must give the right of judgment to the students, and pay attention to cultivating the standardization and organization of students' language. When students express their opinions, click on the relevant content on the courseware, and click on the corresponding aspect when the students talk about it. Contents that students can’t think of should be given timely guidance. After the students express their opinions, systematically summarize the properties of the image of y=x2 and display it on multimedia. It is necessary to put in and out.

The image has an intersection point with the x-axis. This intersection point is also the intersection point of the symmetry axis and the parabola. It is called the vertex of the parabola. It is also the lowest point of the image, with coordinates (0, 0).

Because the graph has the lowest point, the function has a minimum value. When x=0, y minimum=0.

3. Explore the properties of parabola y=-x2

Think about it:

(1) What is the shape of the graph of the quadratic function y=-x2? Think about it first, then make a picture of it.

(2) Can you tell its nature similarly?

Varied training to consolidate and improve

1. On the graph of the quadratic function y=x2, the coordinates of the point symmetrical to point A (-5, 25) are .

2. Points (x1, y1) and (x2, y2) are on the parabola y=-x2, and x1 > x2 > 0, then y1__y2.

3． Assume that the area of ​​a square with side length xcm is ycm2, y is a function of x, and the graph of this function is among the following graphs ( )

Through today's study, have you gained some new understanding of the quadratic functions y=x2 and y=-x2? Can you share your thoughts?

Teacher-student behavior: The teacher poses questions and the students summarize the main content learned in this lesson. Based on the students' summary, multimedia is used to display their differences and connections.

Assign homework and broaden horizons

1. Complete the reading and after-class exercises. Interested students will collect any examples related to parabolas in familiar environments after class.

2. Experience your successful experience in this class, keep a good math diary, and communicate with classmates.

Design intention: By reading and collecting examples related to parabolas in familiar environments after class, students can broaden their horizons; allowing students to write "mathematical diaries" in the form of homework can cultivate students' ability to summarize and gradually develop good study habits.

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For more information about the PPT courseware "Quadratic Functions and Parabolas", please click the Quadratic Functions and Parabolas ppt tag.

"Getting to Know Parabolas" Quadratic Function PPT Courseware 5:

"Getting to Know Parabolas" Quadratic Function PPT Courseware 5 Learning Objectives 1. Be able to use the point tracing method to draw the graphs of quadratic functions y=x and y=-x; 2. According to the graphs of functions y=x and y=-x, intuitively Understand its properties. In the quadratic function y=x, what is the law that y changes with the change of x?

"Getting to Know Parabolas" Quadratic Function PPT Courseware 4:

"Getting to Know Parabolas" Quadratic Function PPT Courseware 4 Learning Objectives 1. Explore the process of experiencing the method and properties of the image of the quadratic function y=x2, and gain experience in using images to study the properties of the function. 2. Be able to use the point drawing method to draw y =x2 image, and be able to recognize and...

"Getting to Know Parabolas" Quadratic Function PPT Courseware 3:

"Getting to Know Parabolas" Quadratic Function PPT Courseware 3 Review the past and learn the new 1. The function of general terrain such as y =a x + b x + c (a, b, c are constants a0) is called the quadratic function of x. 2. What functions have we learned? 3． The graph of a linear function is a straight line. 4. ..

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Update Time: 2024-05-30

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