1, using the matching method. It is easier to find the maximum value by transforming the form of quadratic function into the form of vertex or complete square through formula. Collocation method is mainly suitable for quadratic function with quadratic term coefficient of 1. Use vertices. If the vertex coordinate of the quadratic function is (h, k), then when x=h, y takes the maximum value k, and this method is suitable for the case where the vertex coordinate is known.

2. Use the discriminant method. By judging the sign of the discriminant △ = b 2-4ac of the quadratic equation in one variable, we can judge whether the image of the quadratic function intersects with the X axis, thus determining the maximum value. When △ > 0, the image has two intersections with the X axis, the minimum value is the ordinate of the intersection of the Y axis and the maximum value is the ordinate of the intersection of the X axis.

3. Use the monotonicity of the function. By judging the monotonicity of the function, we can find the extreme value of the function and get the maximum value. This method is suitable for complex quadratic function images.

Value of quadratic function

1, an important part of basic mathematics: Quadratic function is an important part of algebra in basic mathematics and plays an important role in cultivating students' mathematical thinking ability and logical reasoning ability. The image and properties of quadratic function, such as symmetry and extreme point, are the basic knowledge of mathematical analysis, algebraic geometry and other courses, which is very important for subsequent learning.

2. Solve practical problems: Quadratic function is widely used in real life. For example, in physics, quadratic function is used to describe physical phenomena such as free fall and elastic collision; In economics, quadratic function is used to analyze economic indicators such as cost, income and profit. In addition, quadratic function is also widely used in engineering, computer science, statistics and other fields.

3. Basis of mathematical modeling: As one of the foundations of mathematical model, quadratic function plays an important role in studying various practical problems. By establishing a quadratic function model, we can approximately describe the changing laws of many natural and social phenomena, so as to better understand the essence of these phenomena.

4. Cultivate mathematical thinking and innovative ability: learning quadratic function is not only to solve specific problems, but more importantly to cultivate mathematical thinking and innovative ability. Through the study of quadratic function, students' ability to observe, analyze, summarize and solve problems can be improved, which will lay a solid foundation for future study and work.