"Applications of Quadratic Functions" PPT

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"Applications of Quadratic Functions" PPT

Part One: Review and Thoughts

What determines whether the graph of a quadratic function intersects with the x-axis?

Determined by the sign of b²-4ac

b²-4ac�0, there are two intersection points

b²-4ac=0, there is only one intersection point

b²-4ac�0, no intersection point

Find the vertex coordinates of the graph of the quadratic function y=10x-5x², the coordinates of the intersection with the x-axis, and draw a rough graph of the function

Application of quadratic functions PPT, part 2 content: problem exploration:

The computer stores data on a disk. The disk is a disk with magnetic material. There are some concentric circular tracks on the disk, called tracks. As shown in the figure, there is a disk with a radius of 45mm.

(1) The radius of the innermost track of the disk is r mm, and every 0.015mm arc length on it is 1 storage unit. How many storage units are there in this track?

(2) The width between each track on the disk must be no less than 0.3mm. The outer circumference of the disk is not a track. How many tracks can this disk have at most?

(3) If the number of storage units in each track is the same as the innermost track. When the radius r of the innermost track is, the storage capacity of the disk is maximum?

Application of quadratic functions PPT, the third part: analysis of examples

Example 1 As shown in Figure 30-4-1, an athlete jumps to shoot a ball 4m (horizontal distance) away from the center of the hoop, and the basketball falls accurately into the hoop. It is known that the route of the basketball is a parabola. When the horizontal distance of the basketball is 2.5m, the basketball reaches the maximum height, and the maximum height is 3.5m.

If the center of the hoop is 3.05m from the ground, what is the height of the basketball when the player releases it?

(1) Please design a rectangular vegetable garden with a 20-meter-long fence.

(2) How to design the rectangular vegetable garden to maximize the area?

As shown in the figure, a 20-meter-long fence is used to surround a rectangular vegetable garden with one side against the wall. Let the width of the vegetable garden be x meters and the area be y square meters.

(1) Find the functional relationship between y and x and the value range of the independent variables;

(2) How to enclose the vegetable garden to maximize its area? What is the maximum area?

Application of quadratic functions PPT, part 4: practice:

1. In order to store materials, a factory needs to enclose a rectangular site with a circumference of 160 meters. How many meters should the length and width of the rectangle be in order to maximize the area of ​​the storage site?

2. The shape of the window is a rectangle with a semicircle on top. The perimeter of the window is equal to 6cm. How should the size of the window be designed so that it can transmit the most light?

2. Use a rectangular iron plate with a width of 1.2m and bend both sides to make a sink. The cross-section of the sink is an isosceles trapezoid with a base angle of 120º. To maximize the cross-sectional area of ​​the sink, how long should its side AB be?

Application of quadratic functions PPT, Part 5: The idea of ​​"application of quadratic functions"

Can you summarize the basic ideas for solving such problems? Communicate with peers.

1. Understand the problem;

2. Analyze the variables and constants in the problem and the relationships between them;

3. Express the relationship between them mathematically;

4. Do mathematical solutions;

5. Check the rationality of the results, expansion, etc.

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Update Time: 2024-10-01

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 2 industry PPT template

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