"Applications of Quadratic Functions" PPT courseware

Description

"Applications of Quadratic Functions" PPT courseware

learning target:

1. Be able to analyze and represent quadratic function relationships in different practical contexts, and use the knowledge of quadratic functions to solve practical problems.

2. Understand how to use the properties of quadratic functions to find the maximum or minimum value in practical problems

Teachers lead

The general form of the analytical expression of a quadratic function is y=ax2+bx+c(a≠0)

The form of y=a(x-h)2+k is y=a(x+b/2a )2+4ac-b2/4a

When the abscissa is -b/2a, the ordinate has the maximum (minimum) value 4ac-b2/4a

Quadratic function and maximum vegetable garden area

Example 1. Build a rectangular vegetable garden with one side against the wall. The sum of the lengths of the three sides not against the wall is 60m. How should it be designed to maximize the vegetable garden area? What is the maximum area?

Solution: As shown in the figure, suppose the width of the vegetable garden is x (m), the area of ​​the rectangular vegetable garden is y (m2), then the length of the vegetable garden is (60-2 x) (m) according to the analytical expression of the function between y and x for

y=x(60-2x)

=-2x2+60x

=-2(x2-30x+225-225)

=-2(x2-30x+225)-225×(-2)

=-2(x-15) 2 +450

∵a=-2�0 ∴When x=15, y has a maximum value, and the maximum value is 450

Therefore, the vegetable garden area is maximum when the width of the vegetable garden is 15 m. The maximum area is 450m2

Communication and thinking: How to use quadratic functions to find the maximum or minimum value in practical problems?

Exchange thoughts

How to use quadratic function to find the maximum or minimum value in practical problems?

First, we should find the analytical formula of the function and the value range of the independent variables.

Then deform it through the formula, or use the formula to find its maximum or minimum value.

Note: The value of the independent variable corresponding to the maximum or minimum value thus obtained must be within the value range of the independent variable.

Compliance testing

1. It is known that the quadratic function y=2(x-2)2+1, when x=__, y takes the most ___ value, which is ___.

2. The image of the quadratic function y=-2(x-4)2+1 opens ____. When x=__, y takes the maximum ___ value, which is ___.

3. An advertising company wants to design a rectangular billboard with a perimeter of 20m. When the value of one side of the rectangle is, the billboard will have the largest area?

Solution Assume that one side of the rectangle is x(m), then the other side is (10-x)m, and the area of ​​the rectangle is ym2. According to the meaning of the question, the analytical formula of the function between y and x is y=x(10-x)

y=-x2+10x

=-(x-5)2+25

∵a=-1<0 ∴When x=5, y has a maximum value, and the maximum value is 25.

Therefore, when one side of the rectangle is 5m long, the billboard area will be the largest, and the maximum area will be 25m2

Exploration 1

y-2x=1 y=2x+1

x=1 (1,3)

y=3

linear equation of two variables linear function

Solution to a linear equation of two variables Coordinates of points on the graph of a linear function

Exploration 2

In the same rectangular coordinate system, draw the graphs of the functions y=-2x+6 and y=3x+1

1. Find their intersection point P and write the coordinates of point P.

2. Do the coordinates of point P fit the equation 2x+y=6?

Does it fit equation 3x-y=-1? Why?

3. Are the coordinates of point P the solution to the equation system 2x+y=6 3x-y=-1?

4. Using the method of drawing function graphs, what are the main steps to solve a system of linear equations of two variables?

Keywords: Teaching courseware for the application of quadratic functions, Qingdao edition ninth grade mathematics volume 2 PPT courseware download, ninth grade mathematics slide courseware download, application of quadratic functions PPT courseware download, .PPT format;

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Update Time: 2024-11-22

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

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