"Quadratic functions and quadratic equations and inequalities" PPT courseware for quadratic functions, equations and inequalities of one variable

"Quadratic functions and quadratic equations and inequalities" PPT courseware for quadratic functions, equations and inequalities of one variable

Part One: Learning Objectives

Master the solution of quadratic inequalities of one variable

Understand the relationship between quadratic equations, quadratic inequalities and quadratic functions

Be able to use quadratic inequalities of one variable to solve relevant practical problems

Quadratic functions and quadratic equations of one variable and inequalities PPT, part 2 content: independent learning

Problem guide

Preview textbooks P50-P54 and think about the following questions:

1. What is the concept of quadratic inequality of one variable?

2. What is the corresponding relationship between quadratic functions and solutions to quadratic equations and quadratic inequalities?

3. What is the process of solving the quadratic inequality ax2+bx+c>0(a>0)?

A preliminary exploration of new knowledge

1. Quadratic inequality of one variable

(1) Generally speaking, we call an inequality that only contains ______ unknowns, and the highest degree of the unknown is ______, called a quadratic inequality of one variable.

(2) The general form of a quadratic inequality of one variable is ____________________ or ____________________ (where a, b, c are all constants, a≠0)

■Instructions from famous teachers

Keywords in the concept of quadratic inequalities of one variable

(1) One element, that is, it contains only one unknown number, and other elements are constants (or parameters).

(2) Quadratic, that is, the highest degree of the unknown must be 2, and its coefficient cannot be 0.

2. zero point of quadratic function

Generally speaking, for the quadratic function y=ax2+bx+c, we call the real number x that makes _______________ the zero point of the quadratic function y=ax2+bx+c.

3. Correspondence between quadratic functions and solutions to quadratic equations and inequalities

■Instructions from famous teachers

Looking at the inner connection between the three "secondary" from two angles

(1) The angle of the function: the quadratic inequality ax2+bx+c>0 means that the function value of the quadratic function y=ax2+bx+c is greater than 0, and the graph is above the x-axis; the solution set of the quadratic inequality ax2+bx+c>0 is the quadratic function graph Like the value range of the independent variable above the x-axis.

(2) The angle of the equation: The endpoint value of the solution set of the quadratic inequality ax2+bx+c>0 is the root of the quadratic equation ax2+bx+c=0.

4. The process of solving quadratic inequalities of one variable

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1)mx2－5x<0 is a quadratic inequality of one variable. ()

(2) The solution set of the inequality x2-2x+3>0 is R.()

(3) If the two roots of the quadratic equation ax2+bx+c=0 are x1 and x2 (x1

The solution set of inequality 3x2-2x+1>0 is ()

A． x－1

C. ∅D． R

The solution set of the inequality ax2+5x+c>0 is x13

A． a=6, c=1 B． a=-6, c=-1

C. a=1, c=1 D． a=-1, c=-6

Quadratic functions and quadratic equations of one variable and inequalities PPT, the third part: interactive lecture and practice

Solve quadratic inequalities of one variable without parameters

Solve the following inequalities:

(1)2x2+7x+3>0;

(2)-4x2+18x-814≥0;

(3)-2x2+3x-2<0;

(4)-12x2+3x-5>0.

regular method

Methods for solving quadratic inequalities of one variable without parameters

(1) If the quadratic equation corresponding to the inequality can be factorized, that is, it can be transformed into the product form of several algebraic expressions, then the solution set of the inequality can be obtained directly from the roots of the quadratic equation and the direction of the inequality sign.

(2) If the quadratic equation corresponding to the inequality can be transformed into a completely square form, no matter what value it takes, the perfect square form is always greater than or equal to zero, then the solution set of the inequality is easy to obtain.

(3) If neither of the above two methods can solve the problem, the general method of finding the solution set of quadratic inequalities of one variable, that is, the discriminant method, should be used.

Quadratic functions and quadratic equations of one variable and inequalities PPT, Part 4: Feedback on achievement of standards

1. The solution set of inequality 3x2-7x+2<0 is ()

A.x132

C.x－122}

2. The solution set of inequality (3x-2)(2-x)≥0 is ()

A.x|23≤x≤2

B.x|x≥2 or x≤23

C.x|32≤x≤2

D.x|-23≤x≤2

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For more information about the PPT courseware "Quadratic Function Equations and Inequalities of a Quadratic Function and Inequalities of a Quadratic Equation", please click the Quadratic Function Equations and Inequalities ppt Quadratic Functions and Quadratic Equations Inequalities ppt tag.

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