"Applications of Quadratic Functions" PPT free download

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"Applications of Quadratic Functions" PPT free download

Part One: Learning Objectives

1. Experience the process of exploring issues such as the maximum profit in the T-shirt sales process, understand that the quadratic function is a mathematical model of a type of optimization problem, and feel the application value of mathematics.

2. Master the quadratic function relationship between variables in practical problems, and use the knowledge of quadratic functions to find the maximum and minimum values ​​of practical problems.

Knowledge explanation

Quadratic function y=a(x-h)²+k(a≠0)

The vertex coordinates are (h,k)

①When a>0, y has a minimum value k

②When a<0, y has the maximum value k

Application of quadratic functions PPT, part 2: analysis of examples

【example】

[Example 1] A store sells T-shirts. It is known that the unit price when purchased in batches is 2.5 yuan. According to market research, the sales volume and sales unit price satisfy the following relationship: within a period of time, when the unit price is 13.5 yuan, the sales volume is 500 pieces, and every time the unit price is reduced by 1 yuan, 200 more pieces can be sold.

Could you please help me analyze, at what unit sales price can I make the most profit?

【Tracking Training】

1. A store sells shirts. It is known that the profit y (yuan) and the unit price x (yuan) of sales satisfy the relationship y=–x2+24x+2 956, then the maximum profit is ______ yuan.

2. A travel agency wants to organize a group to travel to other places. After calculation, the profit y (yuan) and the tour group members x (person) satisfy the relationship y=–2x2+80x+28 400. To maximize the turnover, then There are _______ people in the tour group.

[Example 2] A circular fountain is to be built in Taohe Park. A pillar OA is installed in the center of the pool perpendicular to the water surface. O is exactly in the center of the water surface, OA=1.25m. Water is sprayed outward from the nozzle A at the top of the pillar, and the water flow is at It falls along a parabola with the same shape in all directions. In order to make the water flow shape more beautiful, it is required to design the water flow to reach a maximum height of 2.25m at a distance of 1m from OA.

If other factors are not considered, what is the minimum radius of the pool so that the sprayed water will not fall outside the pool?

【Tracking Training】

1. (Lanzhou High School Entrance Examination) As shown in the picture, Xiao Ming’s father tied a rope between two trees 2 meters apart and made a simple swing for Xiao Ming. The place where the rope was tied was 2.5 meters above the ground. The tree naturally droops in a parabola shape. When the tree with a height of 1 meter is 0.5 meters away from the nearest tree, its head just touches the rope. Then the distance between the lowest point of the rope and the ground is ____ meters.

2. (Qinghai·High School Entrance Examination) A fruit wholesale market distributes a kind of fruit. If the profit per kilogram is 5 yuan, 200 kilograms can be sold every day. After market research, it was found that if the purchase price remains unchanged, if the price per kilogram increases by 1 Yuan, sales volume will be reduced by 10 kilograms.

(1) If the shopping mall wants to ensure a daily profit of 1,500 yuan and at the same time provide benefits to customers, how much should the price increase per kilogram?

(2) If the shopping mall purely considers economic benefits, how much price increase per kilogram of this fruit can make the shopping mall most profitable?

Application of quadratic functions PPT, the third part: in-class training

1. (Zhuzhou High School Entrance Examination) There is a fountain in a square, and water spurts out from the ground. As shown in the figure, with the horizontal ground as the axis and the water outlet point as the origin, a plane rectangular coordinate system is established. The curve drawn by the water in the air is a parabola y=- (x-2)2+4 (unit: meter), then the maximum height of water spray is ( )

A.4 meters B.3 meters

C.2 meters D.1 meters

[Analysis] Choose A. The vertex coordinates of the parabola are (2,4), so the maximum height of the water spray is 4 meters.

2. (Dezhou·High School Entrance Examination) In order to welcome the 4th World Solar City Conference, Dezhou City replaced the street lights on main road sections with solar street lights. It is known that the price of solar street lights is 5,000 yuan per piece, and two merchants currently have this product. Merchant A uses the following method to promote sales: If you purchase no more than 100 street lamps, you will pay at the original price; if you purchase more than 100 lamps at one time, the price will be reduced by 10 yuan for each additional lamp purchased, but the selling price of the solar street lamps must not be lower. At 3,500 yuan/piece. Merchant B will always sell at 80% of the original price. Now buy x solar street lights. If you buy them all from merchant A, the required amount is y1 yuan; if you buy them all from merchant B, the required amount is y2 yuan.

(1) Find the functional relationship expressions between y1, y2 and x respectively.

(2) If the municipal government invests 1.4 million yuan, how many solar street lights can it purchase at most?

3. (Wuhan·High School Entrance Examination) A hotel has 50 rooms for tourists to stay. When the price of each room is 180 yuan per day, all the rooms will be full. When the daily price of each room increases by 10 yuan, there will be one room available. The hotel needs to pay 20 yuan per day for various expenses for each room where tourists live. According to regulations, the daily price of each room shall not exceed 340 yuan. Assume that the house price of each room increases by x yuan every day (x is an integer multiple of 10).

(1) Suppose the number of rooms booked in one day is y, directly write the functional relationship between y and x and the value range of the independent variable x.

(2) Assume that the hotel’s profit for a day is w yuan, and find the functional relationship between w and x.

(3) When how many rooms are booked in a day, the hotel’s profit is maximum? What is the maximum profit?

Application of quadratic functions PPT, Part 4 content: Class summary

The basic idea of ​​​​solving the problem of "when to obtain the maximum profit".

1. List the quadratic function relationship expressions based on actual problems.

2. Find the maximum profit based on the maximum value problem of the quadratic function.

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for the second volume of ninth grade, application of quadratic functions PPT download, .PPT format;

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Update Time: 2024-10-16

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