The example of quadratic function in grade nine mathematics?

The example of quadratic function in grade nine mathematics?

(08 Shanghai) the graph is the graph of quadratic function y = AX2 + BX + C
① The roots of the equation AX2 + BX + C = 0 are X1 = - 1, X2 = 3
③ When x is greater than 1, y increases with the increase of X
What is the right way to say it____ ①②④______ (fill in the number of the correct answer on the line)
2. (08 Tianjin) the parabola is translated upward by 5 units, and the analytical expression of the parabola is ()
A． B． C． D．
3. (08) given a parabola, if the point (, 5) is symmetric with the symmetric axis of the point about the parabola, then the coordinates of the point are (4,5)
(A) Straight line x = 1 (b) straight line x = 3 (c) straight line x = - 1 (d) straight line x = - 3
4. (08 Yiwu, Zhejiang) it is known that if the image of quadratic function is one of the following images, then the value of is
A.－1 B ． 1 C. －3 D. －4
5. (Longyan City) 15. If the image of a known function is shown in the figure, then the following conclusion is correct ()
A．a＞0,c＞0 B．a＜0,c＜0 C．a＜0,c＞0 D．a＞0,c＜0
6. (Lanzhou City, Gansu Province, 2008) 10. The following table is the corresponding value of the independent variable and the function value of the quadratic function. It is judged that the range of a solution of the equation (which is a constant) is ()
6.17 6.18 6.19 6.20
A． B．
C． D．
7. (Lanzhou City, Gansu Province, 2008) 15. In the same coordinate plane, the image of the following four functions (1, 2, 3, 4) can not be obtained by the function image through translation transformation and axisymmetric transformation, and the function is (fill in the serial number)
8. The minimum value of quadratic function is ()
A． B． C． D．
9. (Ningxia Hui Autonomous Region, 2008) 6. As shown in the figure, if the axis of symmetry of the parabola is a straight line and passes through the point (3,0), the value of is
A. 0 B. －1 C. 1 D. 2
10. (Suqian City, Jiangsu Province) in the plane rectangular coordinate system, the image of function and is roughly the same
11. The form of quadratic function is ()
A． B．
C． D．
12. (08) 7. If a (), B (), C () are three points on the graph of quadratic function, then the size relation of a is
A． B．
C． 　 D． 　
2、 Comprehensive problems of quadratic function
1. (08 Beijing) 1. In the plane rectangular coordinate system, the parabola intersects with the axis at two points (the point is on the left side of the point), and intersects with the axis at the point. The coordinate of the point is, after translating the straight line up three unit lengths along the axis, it just passes through two points
(1) The analytic expressions of straight line and parabola are obtained;
(2) Let the vertex of the parabola be, the point is on the symmetry axis of the parabola, and the coordinates of the point are obtained;
(3) Join and find the degree of the sum of two angles
2. (08 Anhui) the acrobatic troupe performs acrobatics. The actor jumps from a on the right end of the seesaw to B on the top of the ladder. The route of his body (as a point) is part of a parabola, as shown in the picture
(1) Find the maximum height of the actor from the ground;
[interpretation]
(2) It is known that the height of the ladder is BC = 3.4 meters. In a performance, the horizontal distance from the ladder to the take-off point a is 4 meters. Is the performance successful? Please explain the reason
[interpretation]
3. (Putian City) 23. (12 points) loquat is one of the famous fruits in Putian. There are 100 loquat trees in an orchard. The average yield of each tree is 40 kg. Now we prepare a variety of loquat trees to improve the yield. However, if there are many kinds of trees, the distance between trees and the number of each tree will be reduced. According to the practical experience, every variety of trees will receive less sunlight, After putting into production, the average output of all loquat trees in the orchard will be reduced by 0.25 kg per tree. Q: how many loquat trees will be planted and the total output of loquat trees in the orchard will be the largest after putting into production? What is the maximum total output?
Note: the vertex coordinates of parabola are
4. (Xiamen, Fujian, 2008) 24. Known: parabola passing through point
(1) The value of the solution;
(2) If, find the vertex coordinates of the parabola;
(3) If, through a point, make a straight line axis, intersect the axis at a point, intersect the parabola at another point, and find the quadratic function corresponding to this parabola. (hint: please draw a diagram to think about it.)
5. (2008 Maoming City) 24. In order to cooperate with the Beijing Olympic Games, a craft factory in our city designed a handicraft with a cost of 20 yuan / piece and put it on the market for trial sale
Sales unit price (yuan / piece) 30 40 50 60 ……
Daily sales volume 500 400 300 200 ……
(1) Take the corresponding values of and in the table above as the coordinates of the points, draw the corresponding points in the plane rectangular coordinate system below, guess the functional relationship between and, and work out the functional relationship; (4 points)
(2) When the unit sales price is fixed, the craft factory will get the maximum profit every day from the trial sale of the craft. What is the maximum profit? (profit = total sales price total cost) (4 points)
(3) According to the regulations of the local price department, the maximum unit price of the handicraft can't exceed 45 yuan / piece. When the unit price is set, the handicraft factory will get the maximum profit every day? (2 points)
6. (Guiyang, 2008) 25. A hotel room department has 60 rooms for tourists to live in. When the price of each room is 200 yuan per day, the room can be full. When the price of each room is increased by 10 yuan per day, there will be a room free. For a room with tourists, the hotel needs to spend 20 yuan per day for each room
The daily price of each room is increased by yuan
(1) The functional relationship between the daily occupancy (rooms) and (yuan). (3 points)
(2) The hotel's daily room charge (yuan) is a function of (yuan). (3 points)
(3) When the price of each room is how much yuan per day, what is the maximum value? What is the maximum value? (6 points)
7. (Zhenjiang City, Jiangsu Province) 22
The graph of quadratic function passes through point
(1) Find the relation of the quadratic function;
(2) Find the vertex coordinates of the quadratic function image;
(3) Fill in the blanks: translate the image of quadratic function at least units along the coordinate axis, so that the vertex of the image is at the origin
8. (08, Jining, Shandong) 26. The line segment with a length of 1 cm moves to the point at the speed of 1 cm / s along the direction of the edge (the point coincides with the point before the movement). The line segment moves at two points when passing through the intersection of the two perpendicular lines, and the time of the line segment motion is s
(1) If the area of is, write the function relation with (write the value range of the independent variable);
(2) Is it possible for a quadrilateral to become a rectangle in the process of line segment movement? If possible, calculate the value at this time; if not, explain the reason;
(3) Why is the triangle of a vertex similar to the triangle of a vertex when the value is set?
9. (08 Liaocheng, Shandong) 25. (full score of 12 points) as shown in the figure, cut out a square of the same size around a piece of rectangular cardboard 10 cm long and 8 cm wide, and then fold it into a cuboid box without cover (the thickness of the cardboard is ignored)
(1) To make the bottom area of the cuboid box 48cm2, what is the side length of the cut square?
(2) Do you feel that the side area of the converted rectangular box will be larger? If so, please find out the maximum value and the side length of the square cut at this time; if not, please explain the reason;
(3) If you cut out two squares of the same size and two rectangles of the same shape and size around the rectangular cardboard, and then convert them into a cuboid box with a cover, is there the case of the largest side area? If so, please find out the maximum value and the side length of the square cut out at this time. If not, please explain the reason
10. (08 Tai'an, Shandong) 25
In order to expand the scale of export, the city decided to implement government subsidies for the cultivation of this kind of vegetables, stipulating that each mu of this kind of vegetables should be subsidized several yuan at one time. According to the investigation, the relationship between the number of mu (MU) and the amount of subsidy (yuan) roughly meets the linear function shown in Figure 1, The export volume is also increasing, but the income per mu of vegetables (yuan) will decrease accordingly, and the relationship between the export volume and the income per mu of vegetables also roughly satisfies the linear function as shown in Figure 2