Because the definition of quadratic function is abstract, from the definition, quadratic function contains an independent variable and a dependent variable, but when sorting out the relationship between independent variable and dependent variable, junior high school students are confused and can't really understand the concept of quadratic function. Simply put, a function with the shape of "y=ax2+bx+c(a≠0)" is a quadratic function, but junior high school students still have great problems in understanding the simple definition in the process of doing the problem. From the basic form of quadratic function to the learning process of function image, it is difficult for junior high school students to understand the function of image, and they will not use the intuition of image to solve problems in the process of doing problems, and they cannot quickly grasp some basic information of quadratic function according to the image of quadratic function.

2 Maximum length of moving line segment parallel to Y axis ".

Because the horizontal coordinates of all points on the line segment parallel to the Y axis are equal (always T), with the help of the analytical formula of the function image where the two ends are located, the vertical coordinates of the two ends are represented by algebraic expressions containing the letter T. Then, according to the height of the two endpoints, the length of the moving line segment is expressed as a quadratic decomposition function with the independent variable t and the opening downward, and the maximum length of the moving line segment can be obtained by using the properties of the quadratic function.

3 Constant problem:

Constant problem in the distance from (1) point to straight line;

Question "Is there a point on the parabola that makes its distance to a fixed straight line equal to a fixed constant?" ;

Firstly, with the help of parabolic analytical formula, the coordinates of moving point are expressed by a letter, and then the equation is established by using the distance formula from point to straight line. By solving this equation, the abscissa of the dispatch point can be found, and then the ordinate of the dispatch point can be found by using the parabolic analytical formula, so as to find the coordinates of the dispatch point on the parabola.

(2) Constant problem in triangle region:

Question "Is there any point on the parabola that makes the area of the moving triangle formed by it and the fixed line segment equal to a constant?" ;

First, find out the length of the fixed line segment, then express the distance from the dispatching point (whose coordinates need to be expressed in letters) to the fixed line, then establish an equation with the area formula of the triangle, and solve this equation, then you can find out the abscissa of the dispatching point, and then use the analytical formula of the parabola to find out the ordinate of the dispatching point, thus finding out the coordinates of the moving point on the parabola.