Name _ _ _ _ _ _ _ _ _
First, multiple-choice questions (***30 points)
1. The symmetric equation of quadratic function y=x2+4x+c is ().
A.x =-2 b.x =1c.x = 2 d. It is determined by the value of c.
2. Suppose that the parabola y=ax2+bx+c passes through the origin and the first, second and third quadrants, then ()
A.a & gt0，b & gt0，c & gt0 B.a & lt0，b & lt0，c = 0 C.a & lt0，b & lt0，c & gt0d . a & gt； 0，b & gt0，c=0
3. If (2,5) and (4,5) are two points on the parabola y = ax2+bx+c, then its symmetry axis equation is ().
a . x =- 1 b . x = 1 c . x = 2d . x = 3
4. If the intersection of a straight line y=x-n and a parabola y = x2-x-n is on the x axis, then the value of n must be ().
A.0 B.2 C.0 or 2 D. Any real number.
5. The image of quadratic function y = ax2+bx+c is as shown in the figure, so point ().
() In Cartesian coordinate system
A. The first quadrant B. The second quadrant
C. The third quadrant D. The fourth quadrant
6. If the vertex of the parabola y=x2-8x+c is on the X axis, then c is equal to ().
A.- 16 B- 4 c . 8d . 16
7. It is known that a part of the image with parabola y= (as shown in the figure) is in a straight line with x again.
The coordinates when the axes intersect are ()
A.(5，0) B.(6，0 ) C.(7，0) D.(8，0)
8. As shown in the figure, in the images of four quadratic functions, ① y = ax2; ②y = ax2；
③y = cx2； ④ y = cx2。 Then the relationship between a, b, c and d is ().
A.a & gtb & gtc & gtd B. a & gtb & gtd & gtc C.b & gta & gtc & gtd D.b & gta & gtd & gtc
9. It is known that the vertex coordinate of parabola y=-x2+mx+n is (-1, -3).
The values of m and n are () respectively.
A.2，4 B.-2，-4 C.2，-4 D.-2，0
10. parabola y=x2-(m+2)x+3(m- 1) and x axis ().
A. there must be two intersections. There is only one intersection.
C. there are two or one intersection. D. no intersection
Two. Fill in the blanks (***24 points)
1 1. parabola y = ax2+bx+c as shown in the figure, then it is a parabola symmetrical about x axis.
The analytical formula is.
12. If the parabola y = x2+(k- 1)x+(k+3) passes through the origin, then k=.
13. If the abscissa of the vertex of the image with the function y = ax2+4x- is L, then the value of a is.
14. Given that the abscissa of the vertex of parabola y = ax2+ 12x- 19 is 3, then a=.
15. The symmetry axis of parabola y = a(x-k)2+m is a straight line with vertex coordinates of.
16. If the vertex coordinate of parabola y = 2x2+bx+c is (2, -3), then b=, c=.
Iii. Answering questions (*** 46 points)
17.(8 points) Translate the parabola y=ax2+bx+c to the left by 2 units, and at the same time, translate it down by l units, so that it coincides with the parabola y=2x2+4x+ 1. Find the values of a, b and c and draw a more accurate diagram.
18.(8 points) It is known that the image of quadratic function passes through (3,0) point and (2,3) point, and the symmetry axis X = L, so as to find the analytical expression of this function.
19.( 12 points) The image of the known function y = x2+bx- 1 passes through (3,2).
(l) Find the analytic expression of this function; (2) Draw its image and point out the vertex coordinates of the image;
(3) when x >; 0, find the range of x of y 2.
20.(8 points) It is known that the vertex coordinate of parabola is M(l, -2) and the passing point is n (2, 3). Find the analytic expression of this quadratic function.
21.(10min) Part of the image of the quadratic function y=ax2+bx+c is shown below. It is known that its vertex m is in the second quadrant, and the image of this function passes through point A (l, 0) and point B (0, 1).
(1) Please judge the range of real number A and explain the reason;
(2) Let the other intersection of the image of this quadratic function and the X axis be C, and when the area of △AMC is 1.25 times that of △ABC, find the value of A. 。
Quadratic function level test questions (1)
First, multiple-choice questions (let you count less, want you to think more, just choose one to find it! 3 points for each small question, ***30 points)
3. There are two propositions about ⊙M and parabola with (-1, 0) as the center and 1 as the radius:
(1) parabola and ⊙ m do not intersect.
⑵ If the parabola is translated down by 3 units, the parabola will intersect with ⊙ m. 。
Then the following conclusion is correct ().
(a) Only the proposition (1) is correct; (b) Only proposition (2) is correct.
(c) Propositions (1) and (2) are correct; (d) The propositions (1) and (2) are incorrect.
5. The image of the function is shown in the figure, so the situation about the root of the equation is ().
(a) There are two unequal real roots; (b) There are two real roots with different signs.
(c) There are two equal real roots; (d) There is no real root.
6. It is known that there are three points A (,), B(2,) and C (-,) on the image of quadratic function, so the size relationship of, is ().
(A) (B) (C) (D)
8. The image of quadratic function y=ax2+bx+c is shown in the figure, so the following judgment about the relationship between A, B and C is correct ().
(A)ab & lt； 0 BC<0 (c) A+B+C > 0(D)a-b+ c & lt； 0
9. If the straight line passes through the first, third and fourth quadrants, the vertex of the parabola must be in ().
(a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant
10. Pop up a ball vertically at a speed of 20m/s, and its height (h(m)) in the air satisfies the relationship with time (s): h=20t-5t2. When h=20, the movement time of the ball is ().
20s (B)2s (C) (D)
Fill in the blanks (concise results express your keen thinking and need to be careful! 3 points for each small question, ***30 points)
12. Try to write out the analytical formula of a parabola with an upward opening, a straight axis of symmetry and a coordinate of _ _ _ _ _ _ _ _ _ _ _ _ _ _.
13. The temperature M(℃) of an object from 7 am to 4 pm is a function of time t (h): m = (where t = 0 means noon 12 and t = 1 means afternoon 1), then the object is in the morning1.
14. It is known that the image of function ① intersects the axis at point A and point B, there is a point C on the parabola above the axis, and the area of △ABC is 10, then the coordinate of point C is _ _ _ _ _ _ _ _ _ _ _ _.
15. The parabola intersects with the positive semi-axis of the X axis at points A and B, and intersects with the Y axis at point C. If the length of line AB is 1 and the area of △ABC is 1, then the value of b is.
16. Cut a square with a side length of 6 cm (x < 6), and the areas of the other four squares are y, and the functional relationship between y and x is _ _ _ _ _.
18. If the parabola and the X axis intersect at point A and point B respectively, the length of AB is.
19. The quadratic function is converted into.
20. Xiao Wang designed a computer program. Input and output data are as follows:
Enter ... 1 2345 ...
Output … 2 5 10 17 26 …
If the input data is X, the output data is Y, and Y is a quadratic function of X, then the functional expression of Y and X is _ _.
Third, solve the problem (patient calculation, careful observation, show your budding wisdom! 8 points for each small question, ***40 points) Please answer the following questions:
(1) If V is represented by an algebraic expression containing X, then V=
(2) Complete the following table: (4 points)
x(?) 1 2 3 4 5 6 7
V(㎝3) 196 288 180 96 28
(3) Observing the above table, does the value of volume V increase with the increase of x value? When x takes what value, the value of volume v is the largest?
24. Known quadratic function.
(1) Verification: For any real number m, the quadratic function image always has a common point with the X axis;
(2) If the quadratic function image and the X axis have two common points A and B, and the coordinate of point A is (1, 0), find the coordinate of point B. ..
25. A factory has 80 machines, and each machine produces an average of 384 products every day. Now it is planned to add a batch of similar machines to increase the total output. During the trial production, it is found that each machine will produce an average of 4 products less every day because other production conditions have not changed.
(1) If X machines are added, and the total daily production is Y pieces, please write the relationship between Y and X. (2) How many machines can be added to maximize the total daily production? What is the maximum total output?
Fourth, answer questions (reasonable reasoning, accurate expression, show your smart temperament! Each small question 10, ***20)
26. The products produced by a factory cost 2 yuan, and the price is 3 yuan. The annual sales volume is 6,543,800 pieces. In order to get better benefits, manufacturers are prepared to spend some money on advertising; According to statistics, the annual advertising fee is X (10/00000 yuan), and the annual sales volume of products will be Y times of the original sales volume, and Y is the quadratic function of X. Their relationship is as follows:
X (one hundred thousand yuan) 0 1 2
y 1 1.5 1.8
(1) Find the functional relationship between y and x;
(2) If you look at the total profit minus cost and advertising fee, try to write the functional relationship between annual profit S (10/00000 yuan) and advertising fee X (10/00000 yuan);
(3) If the annual advertising fee is 6,543,800+10,000 ~ 300,000 yuan, what is the advertising fee, and what is the maximum profit for the factory? What is the maximum profit?
27. If the parabola and the X axis intersect at two points A and B, and point A is on the X axis.
On the positive semi-axis of, point B is on the negative semi-axis of X, the length of OA is A, and the length of OB is B.
(1) Find the range of m;
(2) If a∶b=3∶ 1, find the value of m and write the analytical formula of parabola at this time;
(3) Let the parabola in (2) intersect the Y axis at point C, and the vertex of the parabola is m. Q: Does the parabola exist at point P, so that the area of △PAB is equal to 8 times that of △BCM? If it exists, find the coordinates of point P; If it does not exist, please explain why.
Quadratic function level test questions (b)
First, multiple-choice questions (let you count less, want you to think more, just choose one to find it! 3 points for each small question, ***30 points)
1. The following function is not a quadratic function ().
(A)y =(x- 1)(x+2)(B)y =(x+ 1)2(C)y = 2(x+3)2-2 x2(D)y = 1-x2
3. The symmetry axis of parabola is ().
Straight line straight line straight line straight line straight line straight line straight line.
4. The opening direction, symmetry axis and vertex coordinates of the quadratic function image are () respectively.
(a) The opening is downward, the symmetry axis is, and the vertex coordinates are (3,5).
(b) The opening is downward, the symmetry axis is, and the vertex coordinates are (3,5).
(c) The opening is upward, the symmetry axis is, and the vertex coordinate is (-3,5).
(d) The opening is upward, the symmetry axis is, and the vertex coordinate is (-3,5).
7. Given the function (), the following four judgments are given: ①; ② ; ③ ; (4) With three of the judgments as the conditions and the remaining one as the conclusion, four propositions can be obtained, among which the number of true propositions is ().
1 (B)2 (C)3 (D)4。
8. Whether m is any real number or not, the total passing point of the image of quadratic function y =+(2-m) x+m is ().
(A)( 1，3) (B)( 1，0) (C)(- 1，3) (D)(- 1，0)
9. Because of being polluted by ink, only the following words can be seen in a math problem:
Know the image intersection of quadratic function (1, 0) ... Prove that the image of quadratic function is symmetrical about a straight line.
According to the existing information, the property that the quadratic function in the problem does not have is ().
The vertex of (a) (3,0) (b) is (2,2).
(c) The length of the line segment cut on the shaft is 2; (d) The intersection with the axis is (0,3).
Fill in the blanks (concise results express your keen thinking and need to be careful! 3 points for each small question, ***30 points)
12. If points P( 1,) and Q (- 1,) are all on a parabola, then _ _ _ _ _ _ _ _ _ _ _ _.
13. Given that the abscissa of the vertex of a parabola is 2, the value of is _ _ _ _ _ _ _ _.
14. Assuming that the image of a quadratic function passes through point A (0) and is symmetrical about a straight line, the analytical formula of this quadratic function may be _ _ _ _ _ _ _ _ _ _ _ _ (only one possible analytical formula is needed).
15. It is known that there are two intersections between a parabola and an axis, and these two intersections are on both sides of a straight line, so the range of values is _ _ _ _ _ _ _ _ _.
16. Write a quadratic function in the form of _ _ _ _ _ _ _ _ _ _ _.
On the plane of 17, there are countless parabolas passing through points A (2 2,0) and b (0,0-1). Please write the analytical formula of one of the parabolas (excluding the letter coefficient): _ _ _ _ _ _ _ _ _ (written as a general formula).
18. Given that the intersection of the function y=x2-200 1x+2002 and the x axis is (m, 0), (n, 0), then (m2-2001m+2002) (N2-200/.
19. If the vertex of the parabola y=-4x2+ 16x- 15 is A, and the intersection with the X axis is B and C, then the area of △ ABC is _ _ _ _ _ _ _ _.
20. The annual output of the product does not exceed 65,438+0,000 tons, and the function image between the annual output of the product (unit: tons) and the cost (unit: ten thousand yuan) is a part of a parabola with the vertex as the origin (as shown in Figure 26-2); The function image between the annual sales volume (unit: ton) and the sales unit price (unit: ten thousand yuan/ton) of this product is a line segment (as shown in Figure 26-3). If all the products produced can be sold in the same year, the gross profit will be the largest when the annual output is _ _ _ _ _ tons (gross profit = sales-expenses).
Third, solve the problem (patient calculation, careful observation, show your budding wisdom! 8 points for each small question, ***40 points)
2 1. Given that the image of a quadratic function passes through, the distance between the symmetry axis and the intersection of parabola and axis is 4. How to find the analytical expression of this quadratic function?
22. As shown in the figure, the straight line y=2x+2 intersects the X axis and the Y axis at points A and B respectively. Rotate △AOB 90 degrees clockwise around point O to get △A 1OB 1.
(1) Draw △ a1ob1in the diagram;
(2) Find the analytical expressions of parabola passing through point A, A 1 point and B 1 point.
23. A fruit wholesale mall sells a high-grade fruit. Profit per kilogram 10 yuan, you can sell 500 kilograms every day. According to market research, if the price per kilogram increases by 1 yuan, the daily sales will be reduced by 20 kilograms.
(1) At present, shopping malls should ensure a profit of 6,000 yuan per day, and at the same time, let customers get benefits, so how much is the price increase per kilogram?
(2) From a purely economic point of view, how much price increase per kilogram of this fruit will maximize the profit of shopping malls?
24. As shown in the figure, the parabola y =-x2+x+6 intersects with the X axis at points A and B, and intersects with the Y axis at point C. 。
(1) Find the area of △ABC;
(2) Given a given point E (o, -3), take the point D on the parabola of the first quadrant and connect DE, so that DE is equally divided by the X axis. Try to determine the shape of the quadrilateral ACDE and prove your conclusion.
25. Known functions
(1) Find the minimum value of the function;
(2) Draw the image of the function in the given coordinate system;
(3) Let the intersection of the function image and the X axis be a (x 1, 0) and b (x2, 0).
Fourth, answer questions (reasonable reasoning, accurate expression, show your smart temperament! Each small question 10, ***20)
26. It is a rectangular piece of paper placed in a plane rectangular coordinate system, with an origin, points on the axis and points on the axis.
(1) As shown in the figure, take a point on it, and after the edge is folded, the point falls on the axis and is recorded as a point. Find the coordinates of the point;
(2) Find the analytical formula of the straight line where the crease is located;
(3) If the parabola passes through this point, find the analytical formula of the parabola, and judge whether the circle with the origin as the center and the radius has an intersection with the parabola except the intersection. If yes, please write down the coordinates of the intersection directly.
27. The road halfway up the mountain is one of the remarkable features of the Shanghai-Chengdu-West Expressway. There are 37 tunnels in the whole line, with a total length of 742421.2m. The cross section of Miaoya tunnel under construction is shown below, which consists of a parabola and a rectangle. The total width of the roadway CD is 8m, and the one-way tunnel has two lanes.
(1). Establish a suitable plane rectangular coordinate system and get the analytical formula of tunnel arch parabola;
(2) Install a street lamp 3 meters away from the ground on both sides of the tunnel arch, and use coordinates to indicate the position of 1 street lamp in the plane rectangular coordinate system of (1);
(3) In order to ensure driving safety, it is required that the height difference between the top of the driving vehicle (set as flat roof) and the tunnel arch in the vertical direction should be at least 0.5m.. After loading the goods, the width of the existing car is meters, and the distance between the top of the loaded goods and the road surface is 2.5 meters. Can the car pass through this tunnel? Please explain the reason.
The ninth grade mathematics quadratic function examination paper
Multiple choice questions: 3 points for each question, *** 15 points. There are four answers to each question, only one of which is correct.
The opening direction, symmetry axis and vertex coordinates of the parabola under 1. are ()
A, the opening is upward; x =-3； (-3,5 5) b, with upward opening; x = 3； (3,5)
C, the opening is downward; x = 3； (-3, -5) D, with downward opening; x =-3； (3,-5)
2. The vertex of parabola y=x2+3x is in ().
A. The first quadrant B. The second quadrant
C. The third quadrant D. The fourth quadrant
4. The distance from the parabola y=x2-2x-3 to the axis is ();
A.4 B.3 C.2 D. 1
Fill in the blanks: (4 points for each small question, ***20 points).
6. When m, the function is a quadratic function.
7. It is known that the image of quadratic function y = (m-2) x2+m2-m-2 with x as independent variable passes through the origin, then m=, and when x increases, y decreases.
8. If both point A (-5, y 1) and point B (2, y2) are on y=2x2, then _ _ (fill in ">" or "
9. If the minimum value of the function is 3, then =; The value of quadratic function is always a number;
10. When drawing the image of quadratic function with "tracing point method" in the third grade mathematics textbook, the following table is listed:
Answer the question according to the information in the table: when the quadratic function.
Iii. Answer: (6 points for each small question, 30 points for * * *)
1 1. It is known that the vertex of the parabola is (-1, -2), and it passes through (1, 10). Find the quadratic function relation corresponding to this parabola.
12. It is known that the parabola passes through three points: (0, -2), (1, 0), (2, 3). Find the quadratic function relation corresponding to this parabola.
13. Known parabola y = x2+x-. Try to find its vertex coordinates and symmetry axis.
14. Enclose a rectangular field with a 40-meter fence. What are the length and width of the maximized area?
15. Find the coordinates of the intersection point between the image of quadratic function y=x2-2x- 1 and the X axis.
Fourth, answer questions (7 points for each small question, 28 points for * * *).
19. When the car is running, it must slide forward for a certain distance after braking before stopping. We call this distance "braking distance", which is an important factor in analyzing accidents. On a curve with a speed limit of 40 b, two cars, A and B, walked in opposite directions and found that the situation was wrong. Brake at the same time, but still collided. The braking distance of a car was measured at the scene afterwards as 6544. The braking distance of car B is greater than 10m, but less than 20m. According to relevant data, the braking distance S A (m) of car A has the following relationship with the vehicle speed X (), where S A = 0. 1x+0.0 1x2. The relationship between the braking distance S B (m) of car B and the vehicle speed X () is shown in the following figure.
5. Answer: (9 points for each small question, ***27 points).
20. In 2000, Shen Ying Automobile Refitting Factory of Dongfeng Company developed Type A agricultural vehicles with a cost of 20,000 yuan/vehicle, an ex-factory price of 24,000 yuan/vehicle and an annual sales volume of 1 10,000 vehicles. In 2006, 5438+0, in order to support the development of ecological agriculture in the western region, the factory seized the opportunity to develop enterprises and comprehensively improve the scientific and technological content of type A agricultural vehicles. The cost growth rate of each agricultural vehicle is X.
(1) Find out the functional relationship between the annual profit y (ten thousand yuan) and x from the sales situation of type A agricultural vehicles in this factory in 200 1 year.
(2) If the annual profit of selling Type A agricultural vehicles in 200 1 year reaches 40.28 million yuan, how many vehicles should be sold in that year? (6 points)
2 1. With the rapid development of urban construction in Huizhou in recent years, the demand for flowers and trees has also increased year by year. A gardening expert plans to invest in planting flowers and trees. According to the market survey and forecast, the profit of planting trees is directly proportional to the investment, as shown in figure 12-①. The relationship between profit and investment in flower planting is quadratic, as shown in figure 12-② (note: the unit of profit and investment is 10,000 yuan).
(1) Find the functional relationship between profit and investment;
(2) If this specialized household invests 80,000 yuan to plant flowers and trees, how much profit can it get at least? What is the maximum profit he can get?
22. As shown in figure 14, parabola intersects with axis at one point, one point, straight line intersects at one point, and straight line intersects with axis at one point.
(1) Write the analytical formula of the straight line.
(2) the area to be searched.
(3) If a point moves from the direction at a speed of 1 unit length per second on a line segment (it does not coincide with it), and at the same time, the point moves from the direction at a speed of 2 unit lengths per second on a ray. Let the movement time be seconds, please write the functional relationship between the areas of and, and find out how long the point has been moving and what is the maximum area.
Chapter 22 Quadratic Function and Inverse Proportional Function
Title: 22.3 Images and Properties of Quadratic Function (V) —— Finding the Analytic Formula of Quadratic Function (P20 ~ P2 1) by the Method of Undetermined Coefficient.
First, the learning objectives:
1, according to the known coordinates of three points on the parabola, the analytical formula of the parabola will be obtained;
2. According to the vertex, the analytical expression of parabola can be obtained when the vertex coordinates are known.
Second, knowledge review:
1 and parabola are two common analytical formulas: (1) The general formula is:, (2) The vertex is:.
3. The intersection coordinates of the straight line L and the two coordinate axes are A (-3,0) and B (0 0,4) respectively. Find the expression of the function corresponding to the straight line l;
Third, autonomous learning:
Find the analytical formula of parabola according to the following steps:
1, the image of the known quadratic function passes through three points: A (0 0,3), B (1, 3) and C (- 1, 1), and the analytic expression of the quadratic function is obtained.
Solution: Let the analytic formula of quadratic function be, and substitute the coordinates of points A, B and C to get:
To solve this system of equations:
∴ The analytic formula of quadratic function is:
2. Given that the vertex coordinate of a parabola is (1, -6) and the parabola passes through point (2, -8), find the analytical formula of the parabola.
Solution: The vertex coordinate of the ∵ parabola is (1, -6), and the ∴ parabola can be set as the vertex.
Replace point (2, -8) with:, ∴a=
The analytical formula of parabola is, that is, (simplified to a general formula).
Fourth, learn to perform:
1. Find the analytical formula of parabola according to the following conditions:
(1) image passing points (-1, -6), (1, -2), (2, 3);
(2) The vertex coordinates of the image are (-1,-1), and the ordinate intersecting with the Y axis is-3;
Verb (abbreviation of verb) ★ Extension and upgrade:
1. If the vertex coordinate of parabola is (1, 3), the opening size is the same as that of, but the direction is opposite, then the analytic expression of quadratic function.
2. As shown in the figure:
(1) Find the analytical formula of parabola;
(2) Answer according to the diagram: When the range of x is, the function value is greater than 0.
3. It is known that the image of the quadratic function intersects the X axis at two points A (-2,0) and B (3 3,0), and the maximum value of the function is 2.
(1) Find the analytic expression of quadratic function image;
(2) Let the vertex of the quadratic function be p, and find the area of △ABP.
Application of Quadratic Function (1) Exercise
1, (Guiyang, 2008) (the full mark of this question is 12)
The hotel housekeeping department has 60 rooms for tourists to live in. When the price of each room is 200 yuan per day, the room will be full. Each room will be increased by RMB 65,438+00 per day, and one room will be given as a gift. There are rooms for tourists, and the hotel needs to pay various fees for each room in 20 yuan every day.
Let the daily price of each room increase by RMB. Q:
(1) The daily occupancy of the room (room) is a function of (yuan). (3 points)
(2) The daily room rate of the hotel (yuan) is a function of (yuan). (3 points)
(3) the functional relationship between the daily profit (yuan) and (yuan) of the housekeeping department of this hotel; When the price of each room is several yuan per day, there is a maximum. What is the maximum value? (6 points)
2. (Guilin in 2008) Guilin Red Bridge is located on the taohuajiang, which is a beautiful scenery of Guilin's two rivers and four lakes. As shown in the figure, a part of the bridge section can be regarded as a parabola passing through three points A, C and B, and a rectangular coordinate system is established with the horizontal line of the bridge deck as the X axis and the straight line passing through the vertex C of the parabola as the Y axis. It is known that the distance between two adjacent columns perpendicular to the bridge deck is 2m (line segment AD is used in the figure).
(1) Find the analytical formula of parabola passing through three points A, B and C.
(2) Find the column height AD.
3. (In 2008, the purchase price of a commodity was 30 yuan/piece, but now it is 40 yuan/piece, and it can be sold 150 pieces every week. Market research shows that if the price of each piece increases by 1 yuan (the price of each piece cannot be higher than that of 45 yuan), then 10 pieces will be sold less every week. We assume that the price of each commodity is RMB (non-negative integer) and the weekly sales volume is RMB.
(1) and the functional relationship with the domain of independent variables;
⑵ How to set the price to maximize weekly profit and increase weekly sales? What is the maximum profit per week?
4. (in 2008? Nanning) With the rapid development of urban construction in recent years, the demand for flowers and trees is increasing year by year. A gardening expert plans to invest in planting flowers and trees. According to the market survey and forecast, the profit of planting trees is directly proportional to the investment, as shown in figure 12-①. The relationship between profit and investment in flower planting is quadratic, as shown in figure 12-② (note: the unit of profit and investment is 10,000 yuan).
(1) Find the functional relationship between profit and investment;
(2) If this specialized household invests 80,000 yuan to plant flowers and trees, how much profit can it get at least? What is the maximum profit he can get?
5.(08 Liangshan Prefecture) There is an edible wild mushroom in our state. At the time of listing, Li, the foreign manager, bought the wild mushroom 1000 kg at the market price of 30 yuan/kg and stored it in the cold storage. It is predicted that the market price of this wild fungus will increase by 1 yuan per kilogram every day; However, it takes 3 10 yuan to store this batch of wild mushrooms every day, and this kind of wild mushrooms can be stored in the cold storage for up to 160 days. At the same time, 3 kilograms of wild mushrooms are damaged every day and cannot be sold.
(1) Let the market price per kilogram of wild mushrooms be yuan, and try to write the functional relationship between and.
(2) If this batch of wild mushrooms is sold once after storage, let the total sales amount of this batch of wild mushrooms be yuan, and try to write the functional relationship between and.
(3) How many days will Manager Li store these wild mushrooms and then sell them to get the maximum profit?
(Profit = total sales-acquisition cost-various expenses)