The quadratic function is the difficulty of junior high school mathematics and the focus of the middle school entrance examination, and many children are confused as soon as they see the final question. This summary explains definitions, image properties, classic examples, and can be printed and practiced repeatedly with the full version of Word.
Why is the quadratic function difficult? Because it strings together algebra, geometry, and practical applications, one final question can test seven or eight knowledge points. But in turn, as long as the basic nature is thoroughly understood, the question of the quadratic function is actually very regular.
1. The basic nature must be familiar
The direction of the opening, the axis of symmetry, the vertex, and the intersection with the axis of the coordinate, these four elements are the roots of all the topics of the quadratic function. Vertex y = a (x-h) ² + k Most intuitive: h-tube translates left and right, k-tube translates up and down, a-tube opens and is fat and thin. When you see the vertex during the test, you can say the axis of symmetry and the vertex in 10 seconds.
II. Three types of analytical interoperability
The general formula, vertex formula, and intersection formula should be freely switchable. To solve the problem of the analytical formula, give priority to what information the question gives: use the vertex formula for the vertex, use the intersection formula for the two x-axis intersection points, and use the general formula pending coefficient method for the three ordinary points.
3. The most valuable question is the compulsory test
The largest profit, the largest area, and the shortest distance are essentially the vertices of the quadratic function. The key is to list the function relations first, then find the vertex of the formula, and finally check the range of independent variables. Special reminder: When the range of independent variables in the actual problem is limited, the maximum value is not necessarily taken at the vertex, and the endpoint value is compared within the range.
IV. Synthesis of primary and inverse proportional functions
The middle examination often puts the quadratic function and the primary function together: the intersection point (unity equation system), the area (cut and make method), and the position relationship. Such questions can get points as long as the algebraic skills are solid.
Do the example in this summary yourself, and then find a few sets of real questions to test, and the quadratic function can pass.
Tip: The webpage is in preview. Click the green button above to download the full version of Word, which can be printed and edited.
发表回复