"Solving quadratic equations of one variable" PPT courseware of quadratic equations of one variable

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"Solving quadratic equations of one variable" PPT courseware of quadratic equations of one variable

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1. The concept of quadratic equation of one variable

An equation 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.

2. General form of quadratic equation of one variable

ax²+bx+c=0（a≠0）

Transforming the equation (1-x)(2-x)=3-x2 into the general form is: ___________, the coefficient of the quadratic term is ____, the coefficient of the linear term is ____, and the constant term is ____.

Equation (m-2)x|m| +3mx-4=0 is a quadratic equation about x, then ( )

A.m=±2 B.m=2 C.m=-2 D.m≠ ±2

1.What is a square root?

If the square of a number is equal to a, then the number is called the square root of a.

2. What are the properties of square roots?

(1) A positive number has two square roots, and these two square roots are opposites of each other;

(2)The square root of zero is zero;

(3) Negative numbers have no square roots.

What is the direct opening method?

Like solving x2=4, x2-2=0, the method of using the definition of square root to directly take the square root to find the solution to a quadratic equation of one variable is called the direct square root method.

induction

1. What are the characteristics of quadratic equations of one variable that can be solved by the direct square root method?

If a quadratic equation of one variable has the form x2=a (a≥0) or (ax+h)2=k (k≥0), then it can be solved by the direct square root method.

2. What are the general steps for solving quadratic equations of one variable using the direct square root method?

First, transform the quadratic equation into a completely square form containing unknown numbers on the left and a non-negative number on the right, and then use the concept of square roots to solve it.

3. Can any quadratic equation of one variable be solved by the direct square root method? Please give an example.

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For more information about the PPT courseware "Quadratic Equations of One Variable and Solving Quadratic Equations of One Variable", please click the "Quadratic Equations of One Variable Equation ppt Solution of Quadratic Equations of One Variable" ppt tag.

"Solving Allocation Methods for Quadratic Equations of One Variable" PPT courseware:

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"Factorization Method for Solving Quadratic Equations of One Variable" PPT courseware:

"Factorization Method for Solving Quadratic Equations" PPT courseware uses the factorization method to solve quadratic equations. General steps: (1) Change the right side of the equation to zero; (2) Decompose the left side of the equation into two linear equations. ________ of factors; (3) Let each factor be zero, we get..

"Formula Method for Solving Quadratic Equations of One Variable" PPT courseware:

"Formula Method for Solving Quadratic Equations of One Variable" PPT courseware 1. For the quadratic equation ax2+bx+c=0(a0), when b2-4ac0, its root is x=________. This formula is called the ________ formula of the quadratic equation. Use the root formula to solve quadratic equations of one variable..

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Update Time: 2024-07-04

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 1 industry PPT template

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