First, the function introduction
1, quadratic function refers to a polynomial function whose highest degree is quadratic. The quadratic function can be expressed as f (x) = ax 2+bx+c (a is not 0). Its image is a parabola, and its principal axis is parallel to the Y axis. Function is a mathematical term. In algebraic expressions, each value of x corresponds to only one value of y, which means that y is a function of X.
2. The definition of function is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concepts is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.
3. The modern definition of a function is to give a set of numbers A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another set of numbers B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of a function includes three elements: the domain A, the domain B and the corresponding rule F, among which the core is the corresponding rule F, which is the essential feature of the function relationship.
4. The function was originally translated by Li, a mathematician of the Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, a function means that one quantity changes with another, or a quantity.
Properties of Quadratic and Quadratic Functions
The images of 1 and quadratic function are parabolas, but parabolas are not necessarily quadratic functions. The parabola of the opening up or down is a quadratic function. Parabola is an axisymmetric figure. The symmetry axis is a straight line x=-b/2a.
2. Quadratic coefficient A determines the opening direction and size of parabola. When a>0, the parabolic opening is upward; When a<0, the parabolic opening is downward. The larger |a|, the smaller the opening of parabola; The smaller the |a|, the larger the opening of the parabola.
3. Both the linear coefficient b and the quadratic coefficient a*** determine the position of the symmetry axis. When A and B have the same number (ab>0), the symmetry axis is on the left side of Y axis; When a and b have different numbers (i.e. AB