Summary of knowledge points of quadratic function in junior high school mathematics: quadratic function: the image and nature of quadratic function are hot and difficult points in the mathematics proposition of senior high school entrance examination. The difficulty of the test questions is generally more difficult. Common choices, fill in the blanks with 3-5 points, and comprehensive questions with 10- 12 points. Investigation contents: ① Through the analysis of the actual problem situation, determine the expression of quadratic function and understand the meaning of quadratic function. (2) We can use familiar ideas such as the combination of numbers and shapes, induction and so on. According to the expression (image) of quadratic function, we can determine the direction of quadratic opening, the axis of symmetry and the coordinates of vertices, and get more information. ③ Comprehensive use of equations, geometric figures, functions and other knowledge points to solve problems. Breakthrough methods: ① correctly understand and master the concept, image and properties of quadratic function. Read more, recite more, and combine graphics. ② Using the idea of the combination of numbers and shapes, with the help of the visualization and properties of functions, we can intuitively solve the problems of the maximum (minimum) value of inequality, the solution of equations, the positional relationship of graphs and so on. (3) Using the idea of transformation, the problem of parabola intersecting with the X axis is solved through the discriminant of the root of a quadratic equation and the relationship between the root and the coefficient. quadratic function

First, multiple choice questions

1.(20 10 A model in Ningyang, Shandong Province) In the plane rectangular coordinate system, the parabola is axisymmetrical about X, and then the parabola is axisymmetrical about Y.. After two transformations, the new parabolic analytical formula is ().

A.B. C. D。

Answer: c

2.(20 10 Jiangxi unified examination sample paper) If the parabola y=2x2 left shift 1 unit, then the parabola obtained is ().

a . y = 2 x2+ 1 b . y = 2 x2- 1 c . y = 2(x+ 1)2d . y = 2(x- 1)2

Answer: c

3.(20 10 Henan senior high school entrance examination simulation question 1) In the school sports meeting, when athletes throw the shot, the distance between the height and the level of the shot thrown is ().

A.6m B. 10m C. 8m D. 12m

Answer: d 4. (20 10 Henan high school entrance examination simulation problem 4) The image of quadratic function () is shown in the figure, and the correct one is ().

None of the answers is correct.

A: A.

5.(20 10 Henan high school entrance examination simulation question 3) Given the image of quadratic function y=ax2+bx+c, the following conditions are correct ().

A.ac0、b0

Answer: d

6.(20 10) The corresponding values of abscissa x and ordinate y of some points on parabola Y = AX2+BX+C are shown in the table.

x … -3 -2 - 1 0 1 …

y …[ -6 0 4 6 6 …

The following statements are given: ① The intersection of parabola and Y axis is (0,6); ② The symmetry axis of parabola is on the right side of Y axis;

(3) Parabola must pass point (3,0); ④ On the left side of the symmetry axis, y decreases with the increase of x 。

As can be seen from the table, the following statement is correct ()

1。

7.(20 10 day simulation) The image of quadratic function y=ax2+bx+c is as shown in the figure, so the following four conclusions ① a about this quadratic function.

1。

Answer: c

8.(20 10 simulates Xiamen Lake) The intersection of parabola = and coordinate axis is ()

A. Two intersections B. One intersection C. No intersection D. Three intersections