1. Establish the consciousness of combining numbers and shapes with coordinate systems.
Judging from the comprehensive problems of quadratic function in the senior high school entrance examination in recent years, most of them are related to coordinate system, which is characterized by establishing the corresponding relationship between points and coordinates. We can study the properties of geometric figures by algebraic method; You can also get the answers to some algebraic problems intuitively with the help of geometric figures.
2. Use straight lines or parabolas to master functions and equations.
Straight line and parabola are images expressed by linear function and quadratic function, which are two important functions in junior middle school mathematics. So no matter how to find its analytical formula and study its properties, it is inseparable from functions and equations.
3. When conditions or conclusions are changeable, pay attention to classified discussion.
Classification discussion is to test the accuracy and rigor of students' thinking, which involves this kind of questions, usually through the variability of conditions or the uncertainty of conclusions. Some problems, if we don't pay attention to the classified discussion of various situations, may cause wrong solutions or missing solutions. In recent years, using classified discussion to solve problems has become a new hot spot.
4. Synthesize multiple knowledge points and flexibly use equivalent conversion.
The transformation thought in junior middle school mathematics generally includes the transformation from known to unknown and from complex to simple. When solving the quadratic function synthesis problem, we should pay attention to the connection and transformation between different knowledge points.
Problem-solving skills of quadratic function in junior high school
1, translation: the shape and opening direction of the figure will not be changed after the translation transformation of the quadratic function image, so the value of a remains unchanged. The position of the vertex will change with the translation of the whole image, so as long as the new vertex coordinates are obtained according to the motion law of the point, the analytical formula can be determined.
2. Axisymmetry: This graphic transformation includes two ways: X symmetry and Y symmetry.
The image of a quadratic function is symmetrical about X axis, but its shape remains the same, but the direction of opening is opposite, so the value of a is the original reciprocal. When the vertex position changes, as long as the new vertex coordinates are obtained according to the coordinate characteristics of the point symmetrical about the X axis, the analytical formula can be determined.
The quadratic function image is symmetrical about Y axis, and its shape and opening direction remain unchanged, so the value of A remains unchanged. However, the position of the vertex will change. As long as the new vertex coordinates are obtained according to the coordinate characteristics of the points symmetrical about the Y axis, the analytical formula can be determined.
3. Rotation: mainly refers to the image transformation with the vertex of the quadratic function image as the rotation center and the rotation angle of180. This rotation will not change the image shape of the quadratic function, and the opening direction is opposite, so the value of a will be the original reciprocal, but the vertex coordinates will remain unchanged, so it is easy to find its analytical formula.