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.

Generally speaking, there is the following relationship between independent variable x and dependent variable y:

general formula

Y = ax 2+bx+c (a ≠ 0, a, b and c are constants), and the vertex coordinates are (-b/2a, (4ac-b 2/4a).

Vertex type

Y = a (x+h) 2+k (a ≠ 0, a, h and k are constants) or y = a (x -h) 2+k (a ≠ 0, a, h and k are constants), and the vertex coordinates are (-h, k) or. The images are the same, and sometimes the topic will point out that the general formula can be turned into a vertex by collocation;

Intersection formula

y=a(x-x 1)(x-x2)

[only applicable to a (X 1, 0) and a (X 1, 0) intersecting the x axis, that is, y=0.

Parabola of b (x2, 0)]

;

To change from general formula to intersection point:

∫x 1+x2 =-b/a

x 1x2=c/a

∴y=ax^2+bx+c=a(x^2+b/ax+c/a)

=a[(x^2-(x 1+x2)x+x 1x2]=a(x-x 1)(x-x2)

Important concepts: a, b and c are constants, and a≠0, a determines the opening direction of the function. A>0, the opening direction is upward; A<0, the opening direction is downward. The absolute value of a can determine the opening size. The greater the absolute value of a, the smaller the opening, and the smaller the absolute value of a, the larger the opening.