"Relationships Described by Quadratic Functions" Quadratic Function PPT Courseware 3

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"Relationships Described by Quadratic Functions" Quadratic Function PPT Courseware 3

Review the past and learn the new

1. What is a function?

In a certain change process, there are two variables x and y. If for every possible value of x, there is a unique y value corresponding to it, then y is called a function of x.

2. What is a linear function?

The form is y=kx+b (k and b are constants, k≠0)

3. What is an inverse proportional function?

The form is y=k/x (k is a constant, k≠0)

think about it

How many orange trees can be planted to maximize the total yield of oranges in the orchard?

Solution: y=(100+x)(600-5x)=-5x2+100x+60000

y=-5(x2-20x)+60000=-5(x2-20x+102-102)+60000

=-5(x-10)2+60500 ≤60500

Definition Generally, a function of the form y=ax2+bx+c (a, b, c are constants, a≠0) is called the quadratic function of x. Among them, ax2 is called the quadratic term, a is called the quadratic term coefficient; bx is called the linear term, b is called the linear term coefficient; c is called the constant term.

For example: y=-5x2+100x+60000

y=100x2 +200x+100

regular method

1. The algebraic expression y=ax²+bx+c regarding the quadratic function expression of x must be an integer, a, b, c are constants, and a≠0.

2. The highest degree of the right side of the equation is 2. It can have no linear terms and constant terms, but it cannot have no quadratic terms.

Summary of this lesson

1. Definition: Generally, a function of the form y=ax²+bx+c (a, b, c are constants, a≠0) is called the quadratic function of x.

2. Several different representations of y=ax²+bx+c (a, b, c are constants, a≠0):

(1)y=ax²(a≠0,b=0,c=0,).

(2)y=ax²+c(a≠0,b=0,c≠0).

(3)y=ax²+bx (a≠0,b≠0,c=0).

3. The essence of the definition is: ax²+bx+c is an integer, the highest degree of the independent variable x is quadratic, and the value range of the independent variable x is all real numbers.

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"Relationships Described by Quadratic Functions" Quadratic Function PPT Courseware 2:

"Relationships Described by Quadratic Functions" Quadratic Function PPT Courseware 2 Dare to Explore What circular patterns have you seen in your life? What does the size of their area depend on? Let the radius of the circle be x and the area be y. (1) Is y a function of x? yes. Because when given a...

"Relationships Described by Quadratic Functions" Quadratic Function PPT courseware:

"Relationships Described by Quadratic Functions" Quadratic Function PPT Courseware Learning Objectives: 1. Experience the process of exploring and representing quadratic functions, and gain experience in using quadratic functions to express the relationship between variables. 2. Be able to determine whether a function is a quadratic function. 3. Can put a two...

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Update Time: 2024-11-22

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