"Quadratic Equation of One Variable" PPT Courseware 5

Description

"Quadratic Equation of One Variable" PPT Courseware 5

teaching objectives:

1. Experience and explore the concept of quadratic equations, and understand the quadratic terms, linear terms, and constant terms in quadratic equations.

2. Understand the general form of quadratic equations and convert quadratic equations into general forms.

3. Cultivate students' awareness of active participation and cooperation, and improve their self-confidence in learning mathematics.

Question 1:

To design a 2m high human body statue, according to relevant examples, it is shown that when the height ratio of the upper part (above the waist) and the lower part (below the waist) of the statue is equal to the height ratio of the lower part to the whole, the harmony and beauty of the statue can be increased. Question : How high should the lower part of the statue be designed?

Question 2:

There is a rectangular piece of paper on the table of the students, 25cm long and 15cm wide. Cut out a similar square in each of its four corners, and then fold the surrounding protruding parts to make a square box without a lid. If you want to make a square box without a lid, The bottom area of ​​the covered square box is 300cm2. Then, how many cm are the sides of the square that should be cut off from each corner of the paper?

Question 3:

The school is going to organize a volleyball invitational tournament. Every two participating teams will have a match. According to the conditions such as venue and time, the schedule is scheduled for 7 days, with 4 games arranged every day. How many teams should the competition organizer invite to participate?

Explore new knowledge

What are the characteristics of equations ① ② ③?

① x2=2(2－x)

②(25-2x)(15-2x)=300

③1/2x(x-1)=28

(1) Both sides of these equations are integers,

(2) The equation contains only one unknown number,

(3) And the highest degree of the unknown is 2.

An equation like this where both sides of the equal sign are integers, contain only one unknown (univariate), and the highest degree of the unknown is 2 (quadratic), is called a quadratic equation of one variable.

Generally speaking, any quadratic equation about x can be transformed into the following form after sorting

ax²+bx+c=0(a≠0)

This form is called the general form of a quadratic equation of one variable.

Among them, ax2 is a quadratic term, a is a quadratic term coefficient; bx is a linear term, b is a linear term coefficient; c is a constant term.

Use your brain

Equation about x (m2-9) x2+(m-3) x +5m-1=0,

(1) When m takes what value, is it a quadratic equation?

m≠±3

(2) When m takes what value, is it a linear equation of one variable?

m=-3

explore

After understanding the quadratic equation, we will next explore the solution to the quadratic equation.

What is the definition of solution to an equation?

The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation

Give it a try:

1. The equation (mx-1)x2+mx+1=0 is a quadratic equation about x, then the value of m is ＿＿＿

A any real number B m≠0

C m≠1 D m≠0 and m≠1

2. Which of the equations about x must be a quadratic equation?

A ax2＋bx＋c＝0 B mx2＋x－m2＝0

C (m＋1)x2＝(m＋1)2 D （m2＋1) x2－m2＝0

Additional exercises:

1. The coefficient of the quadratic term of the quadratic equation 3x2+x=2 is ________, the coefficient of the linear term is ________, and the constant term is ________.

2. Determine whether the equation 3x2-mx (3x+3m-1)=2x+1 about x is a quadratic equation. If so, indicate its quadratic term coefficient, linear term coefficient and constant term.

3. When m has a value, the equation (m+1)x|4m|-2+27mx+5=0 is a quadratic equation of one variable with respect to x.

Summary and Thoughts

1. The concept of quadratic equation of one variable

An integral equation that contains only one unknown and the highest degree of the unknown is 2 is called a quadratic equation.

2. General form of quadratic equation of one variable

Generally, any quadratic equation about x can be transformed into the form ax²+bx+c=0. We call ax²+bx+c=0 (a, b, c are constants, a≠0) General form of quadratic equation.

3. Imitate the definition of a quadratic equation. Can you define a cubic equation? Please give it a try!

Keywords: quadratic equation teaching courseware, Qingdao edition ninth grade mathematics volume PPT courseware download, ninth grade mathematics slide courseware download, quadratic equation PPT courseware download, .PPT format;

For more information about the PPT courseware "Quadratic Equation of One Variable Equation", please click the "Quadratic Equation of One Variable Equation" PPT tab.

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Update Time: 2024-11-24

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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