Practical problems of quadratic function Any one

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• 1. 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 pay 20 yuan per day for each room. Suppose the price of each room is increased by X yuan per day The functional relationship between the daily occupancy y (rooms) and X (yuan); (2) the functional relationship between the daily room charge P (yuan) and X (yuan); (3) the functional relationship between the daily profit w (yuan) and X (yuan) of the room department of the hotel; when the price of each room is how many yuan per day, w has the maximum value? What is the maximum value?
• 2. It is known that the circumference of the rectangle is 36cm, and the rectangle rotates around one of its sides to form a cylinder. When the length and width of the rectangle are respectively, the side area of rotation is the largest?
• 3. Practical problems of quadratic function in junior high school mathematics A supermarket sells a kind of aquatic product with a sales cost of 40 yuan per kilogram. According to market analysis, if it is sold at 50 yuan per kilogram, 500 kg can be sold in a month, and the monthly sales volume will be reduced by 10 kg for every 1 yuan increase in the sales unit price 1) When the unit price is 55 yuan per kilogram, calculate the monthly sales volume and profit 2) Suppose the unit selling price is x yuan per kilogram and the monthly selling profit is y yuan 3) The store wants to make the monthly sales profit reach 8000 yuan under the condition that the monthly sales cost does not exceed 10000 yuan. How much is the sales unit price?
• 4. The cost of a kind of product produced by a company is 2 yuan, the selling price is 3 yuan, and the annual sales volume is 100000 pieces. In order to obtain better benefits, the company is prepared to put out certain funds for advertising. According to experience, when the annual advertising cost is x (unit: 100000 yuan), the annual sales volume of the product will be y times of the original sales volume, and Y is a quadratic function of X. their relationship is shown in the table: X (100000 yuan) Yuan) 012 y11.51.8… (I) find the functional relationship between Y and X; (II) if profit is regarded as total sales minus cost and advertising expenses, try to write the functional relationship between annual profit s (100000 yuan) and advertising expenses x (100000 yuan); (III) if the annual advertising expenses are x, X ∈ [100000, 300000] yuan, ask what range of advertising expenses is, and the annual profit of the company increases with the increase of advertising expenses enlarge?
• 5. When the price of a certain commodity is 15 yuan, 500 items can be sold. For every 1 yuan increase in the price, the number of items sold will be reduced by 20. In order to maximize the amount of sales, the price should be set at______ Yuan
• 6. Translate the parabola y = x ^ 2 + BX + C three unit lengths to the left, and then translate it two unit lengths to the upper, then get the parabola y = x ^ 2 + 3x + 6, and find the values of B and C
• 7. On the ninth grade mathematical problems of quadratic function, a little difficult The quadratic function passes through points B (- 1,0) and C (3,0), its vertex is on the straight line y = kx-1, and the intersection Y axis of the quadratic function is on a 1) Find the axis of symmetry of the quadratic function 2) Finding the coordinates of point a (expressed by the algebraic expression of K) 3) Try to judge whether △ a 0b and △ AOC are similar, if all k values can be obtained It doesn't matter if you can work out a few questions~
• 8. What is the intersection coordinate of parabola y = ax (square) and straight line y = a (square) x (square) (a is not equal to zero)?
• 9. A simple mathematical problem of quadratic function At the beginning, a businessman sold a certain commodity with a purchase price of 8 yuan per piece at 10 yuan per piece, and he could sell 100 pieces per day. He wanted to increase the price to increase the profit. Through the experiment, it was found that the daily sales of this commodity would decrease by 10 pieces per piece with a price increase of 1 yuan. Please write down the functional relationship between the price x (yuan / piece) and the daily profit y (yuan)
• 10. The problem of quadratic function The relationship between the price and time t (unit: day) of a certain commodity in the supermarket in the recent 30 days is (T + 10) yuan, and the relationship between the sales volume and time t is (35-t), where t is greater than 0 and less than or equal to 30, and it is an integer. When does the commodity get the maximum daily sales amount? What is the maximum value?
• 11. Parabola of elementary third quadratic function It is known that there is a point C (0,2) d (4,6) on the x-axis in the plane Cartesian coordinates, and there is a point a whose distance from point C and point D is the smallest Finding the coordinates of point a
• 12. It is known that the straight line y = - 2x + B, B is not equal to 0, intersects with X axis at point B; the analytic formula of a parabola is y = x square - [B + 10] x + C 1. If the parabola passes through point B and its vertex P is on the straight line y = - 2x + B, try to determine the analytical formula of the parabola; If the symmetric axis of the parabola just passes through point C, try to determine the analytical formula of the straight line y = - 2x + B!
• 13. Quadratic function In y = (AX) 2 + BX + C, a determines the opening of parabola b. c.
• 14. Parabolic quadratic function problem It is known that the opening direction, shape and size of a parabola are the same as that of the parabola y = 3x * 2, and the vertex is on the vertex of the parabola y = (x + 2) * 2 Find the analytic formula of this parabola Let y = 3 (x + a) * 2 + B The vertex of parabola y = (x + 2) * 2 is (- 2,0) therefore y=3（x+2）*2 Why not set y = 3x * 2 + a
• 15. Why is a quadratic function a parabola The parabola is that the x-axis advances at constant speed VT, while the y-axis advances at ^ 2. How can we deduce that y is proportional to the square of X
• 16. On the parabola of quadratic function For a parabola composed of three points a (- 1,0) B (3,0) C (0, - 1), the point q is on the Y-axis and the point P is on the parabola For a parabola composed of three points a (- 1,0) B (3,0) C (0, - 1), the point q is on the Y-axis and the point P is on the parabola. If we want to make the quadrilateral composed of point qpab a parallelogram, we need to find the coordinates of point P. sorry, we missed a parallelogram in the above problem
• 17. The relation between quadratic function and parabola? What is the relationship between quadratic function and parabola
• 18. Why is the image of quadratic function a parabola
• 19. A.b.in the formula of parabola in quadratic function
• 20. The parabola image passes through a (0,1) B (1,2) C (2, - 1), and the analytic expression of quadratic function is obtained