Therefore, the way to break through the dilemma of quadratic function learning lies in the students themselves. Students must independently experience the derivative process of quadratic function, actively think and understand the quadratic function problem, and build a complete knowledge framework.
1 Establish analogy ideas and understand quadratic functions.
A deep understanding of quadratic functions, especially the images and properties of functions, is the fundamental force to solve all problems related to quadratic functions. Therefore, students need to actively understand and deeply interpret quadratic functions, and the way to deeply understand them lies in analogy.
Familiar with some simple quadratic function images.
3 Learn to transform functions, for example, Y = 2x 2-4x+3 can be transformed into vertex Y = 2 (x- 1) 2+ 1.
Learn to find the root formula and image of quadratic function.
Experience the process of exploring, analyzing and establishing the quadratic function relationship between two variables, and further experience how to describe the quantitative relationship between variables by mathematical methods.
The quadratic function relationship between variables can be expressed in tables, expressions and images, which can improve organizational thinking and language expression ability. Appropriate methods can be chosen to express the quadratic function relationship between variables according to specific problems.
7 can make images of quadratic functions, and can analyze the properties of quadratic functions according to the images, and gradually accumulate experience in studying the properties of functions.
According to the expression of quadratic function, the open direction, symmetry axis and vertex coordinates of quadratic function can be determined.
Understand the relationship between quadratic equation and quadratic function, and use the image of quadratic function to find the approximate root of quadratic equation.
I hope this helps.