Quadratic function (also called parabola) is a difficult point for students to learn in junior high school. In senior high school, most students think that quadratic function is difficult to learn, because it involves monotonicity of function, definition domain in a certain interval, especially the range of function in a certain interval, and some students don't even know the basic knowledge of general quadratic function. For example, to find the opening direction, symmetry axis, vertex coordinates, maximum value and minimum value of quadratic function, better students can only find it by formula, and will not find the symmetry axis, vertex coordinates, maximum value and minimum value by matching method. In addition, the knowledge of quadratic function in junior high school is not high, which leads to some schools' rough explanation, and even some schools don't even talk about it. So when they went to high school to learn the content of quadratic function in basic elementary function, most of them said they couldn't, and they hadn't learned it, so the teacher had to teach junior high school content again. Therefore, in order to let students learn the content of 1 compulsory basic elementary function well, we take quadratic function as the research object as a teaching case, and how to make a good connection between junior high school transition and new content.
First of all, it is necessary to predict several problems that students will face in this stage of learning:
First, it should be clear that there is a transition between junior high school content and senior high school content.
There are also changes in the way of thinking and teaching ability.
Third, students' study habits and psychology need to adapt to the environmental changes from junior high school to senior high school.
Secondly, the objectives, knowledge points, key problems and abilities of quadratic function are obviously improved compared with those of quadratic function learned in junior high school.
Clear teaching objectives.
The expressions of quadratic functions generally have the following three kinds:
General formula: y = ax2+bx+c (a ≠ 0)
Vertex: y = a (x-h) 2+k (a ≠ 0)
Two formulas (or zero formula): y = a (x-x 1) (x-x2) (a ≠ 0) Understand the function of coefficients A, B and C and their influence on images.
Master the image and properties of quadratic function.
Using nature skillfully to solve practical problems and strengthening the application of the idea of combining numbers with shapes.
When learning the compulsory elementary function of 1, we should carefully review the knowledge of junior high school related functions, find out the similarities and differences, and finally achieve the same goal through different ways.
Choosing exercises should be accurate, and the knowledge used should not only involve junior high school content, but also improve the ability, that is, combine junior high school content with senior high school content to better play the role of cohesion.
Do a good job in the variant training of the topic, draw inferences from one another, make the knowledge of all aspects of quadratic function transition naturally, and realize the seamless connection of knowledge
It is known that the quadratic function f(x) satisfies: f (2) = f (- 1) =- 1, and f(x)max=8. Find the analytical expression of this function.
Variant training: It is known that the image of quadratic function Y = AX2+BX+C passes through the vertex (3,-1), and the point coordinate with the Y axis is (0, 1 1), and the analytical formula of this function is obtained.
The quadratic function f (x) = x2+2ax+2, x∈ is known.
When a =- 1, find the maximum and minimum of the function f(x).
Be realistic about the range of the number A, so that y= f(x) is a monotone function.