Three Expressions of Quadratic Function
General formula: y = ax 2; +bx+c(a, b, c are constants, a≠0)
Vertex: y = a (x-h) 2; +k[ vertex P(h, k) of parabola]
Intersection point: y = a(X-X 1)(X-x2)[ only applicable to parabolas with intersection points a (x 1, 0) and b (x2, 0) with the x axis]
Note: Among these three forms of mutual transformation, there are the following relations:
h =-b/2a k=(4ac-b^2； )/4a x 1，x2 =(-b √b^2； -4ac)/2a
Quadratic function vertex coordinate formula
General formula: y = ax 2+bx+c (a, b and c are constants, and a≠0).
Vertex: y = a (x-h) 2+k
[Vertex P(h, k) of parabola]
For quadratic function y = ax 2+bx+c
Its vertex coordinates are (-b/2a, (4ac-b 2)/4a).
Intersection point: y=a(x-x? )(x-x？ ) [only when it is related to the x axis A(x? , 0) and B(x? 0) parabola]
Where x 1, 2 =-b √ b 2-4ac.
Note: Among these three forms of mutual transformation, there are the following relations:
______
h=-b/2a= (x？ +x？ ) /2 k = (4ac-b 2)/4a Intersection with X axis: X? ，x？ =(-b √b^2-4ac)/2a
Derivation of vertex coordinate formula of quadratic function
General formula: y = ax 2+bx+c (a, b and c are constants, and a≠0).
Vertex: y = a (x-h) 2+k
[Vertex P(h, k) of parabola]
For quadratic function y = ax 2+bx+c
Its vertex coordinates are (-b/2a, (4ac-b 2)/4a).
Arrangement of Important Test Sites of Quadratic Function
Test center: function and function definition domain and related concepts such as function value, function representation and constant function.
Assessment requirements: (1) Understand variables, independent variables and dependent variables through examples, and understand the concept of function, its definition domain and function value; (2) Know the constant function; (3) Know the representation of functions and the meaning of symbols.
Test center: use the undetermined coefficient method to find the analytical formula of quadratic function.
Assessment requirements: (1) Master the method of finding the resolution function; (2) Using the undetermined coefficient method skillfully to find the resolution function.
Pay attention to the steps of solving the resolution function: primary design, secondary generation, three columns and four returns.
Test center: draw the image of quadratic function
Examination requirements: (1) Knowing the meaning of function image, I will draw function image by drawing points in plane rectangular coordinate system; (2) Understand the image of quadratic function and realize the idea of combining numbers with shapes; (3) Can draw an approximate image of quadratic function.
Test center: the image of quadratic function and its basic properties
Assessment requirements: (1) Establish the relationship among linear function, binary linear equation and straight line with intuitive images, and understand and master the properties of linear function; (2) The vertex coordinates of quadratic function are obtained by collocation method, and the related properties of quadratic function are described.
Note: (1) When solving problems, you should combine numbers and shapes; (2) The translation of quadratic function should be transformed into vertex.
The above is the arrangement of the important knowledge points of the quadratic function of mathematics in grade three that I have arranged for you.