Quadratic function is an important content in ninth grade mathematics, which involves the image, nature, analytical formula and maximum value of function. By studying quadratic function, students can better understand the essence and changing law of function and improve their mathematical thinking and problem-solving ability.

In the teaching of quadratic function, the following steps are generally adopted:

1. Introduce a new lesson: introduce the concept and background of quadratic function, and guide students into the learning situation.

2. Explaining examples: Through the explanation of examples, let students understand the images and properties of quadratic function and master the method of solving quadratic resolution function.

3. Organize exercises: let students practice by themselves, consolidate what they have learned by solving problems, and deepen their understanding of quadratic functions.

4. Classroom interaction: interact with students, answer students' questions and give targeted guidance.

5. Summary: Summarize the contents learned in this lesson, sort out the knowledge points, and emphasize the key points and difficulties.

6. Assigning homework: Let students review what they have learned in this lesson at home, and deepen their understanding and consolidation of knowledge by completing homework.

7. Review and consolidation: In subsequent courses, students can deepen their understanding and mastery of the content by reviewing and consolidating the knowledge of quadratic function they have learned before.

8. Class summary: Summarize the contents learned in this chapter, sort out the knowledge points, and emphasize the key points and difficulties.

Properties of quadratic function:

1, opening direction: the quadratic function image is a parabola, and the parabola has different opening directions according to the sign of the quadratic coefficient A. If a>0, the parabola opens upwards; If a

2. Vertex coordinates: The vertex coordinates of the quadratic function image are (h, k), where h=-b/2a and k = (4ac-b 2)/4a. When a>0, the vertex of parabola is below the X axis; When a<0, the vertex of parabola is above the X axis.

3. Symmetry axis: the symmetry axis of the quadratic function image is the Y axis, and the symmetry axis equation is x=-b/2a.

4. Increase or decrease: if a>0, when x≤-b/2a, Y decreases with the increase of X; When x≥-b/2a, y increases with the increase of x, if a

5. Maximum or minimum value: if a >；; 0, when x=-b/2a, y takes the minimum value of (4ac-b 2)/4a; If a