The coordinate formula of the intersection point of quadratic function is y=a(X-x 1)(X-X2). Substituting a, X 1 and x2 into y=a(X-x 1)(X-x2), we can get an analytical formula, that is, y=ax? Factorization of +bx+c, opening brackets, is the general formula. X 1, X2 is a quadratic equation about ax? +bx+c=0, then the intersection points are (x 1, 0) and (x2, 0).

Quadratic function is a mathematical function. The image of this function is a curve symmetrical about a straight line x=-b/2a, which is called the symmetry axis of quadratic function. When the symbols of A and B are the same, the symmetry axis is on the left side of Y axis; When the signs of A and B are different, the symmetry axis is on the right side of the Y axis. In addition, c also affects the intersection of the function image and the y axis.

There are three forms of quadratic function, standard, vertex and general. Standard form refers to a quadratic function with complete form, and its expression is y=ax? +bx+c； Vertex type refers to a quadratic function with vertex coordinates, and the expression is y=a(x-h)? +k； General type refers to a quadratic function that is transformed into a standard or vertex type by matching method.

Quadratic function is widely used in mathematics. It can be used to solve many problems. For example, quadratic function can be used to describe physical phenomena such as free fall, circular motion and parabolic motion, and can also be used to solve the optimal solutions of some practical problems, such as the shortest path problem and profit maximization problem.

In addition, quadratic function is one of the important contents of senior high school entrance examination and college entrance examination. In the senior high school entrance examination, quadratic function usually appears as the last question, which is difficult; In the college entrance examination, quadratic function also occupies a very important position, not only in multiple-choice questions and fill-in-the-blank questions, but also in application questions and comprehensive questions.

The meaning of quadratic function:

1, definition. The general shape is y=ax? The function of +bx+c is called quadratic function.

2. Images and attributes. The images of quadratic function are all parabolas with upward or downward openings, all have symmetry axes perpendicular to the X axis, and all have the highest or lowest vertices.

3. Minimum value or maximum value. When a>0, the minimum value of quadratic function is c; When a<0, the maximum value of the quadratic function is c.

4. Symmetry axis and symmetry center. The symmetry axis of a quadratic function is a straight line x=-b/2a, and the center of symmetry is the vertex.