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

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

General steps for solving quadratic equations of one variable using the formula method:

(1) Change the coefficient of the quadratic term of the equation into ________;

(2) Move the constant term to the ________ side of the equation;

(3) Add the linear coefficient ________ to both sides of the equation;

(4) The formula on the left side of the equation is _________ containing the unknown, and the right side of the equation is a constant;

(5) Take the square root of both sides of the equation and find the roots of the equation.

1. (4 points) (1) The solution of the quadratic equation x2+1=2 is ________;

(2)The solution of equation (x-1)2=4 is ________.

2. (4 points) (2013·Lishui) The quadratic equation of one variable (x+6)2=16 can be transformed into two linear equations of one variable. One of the linear equations of one variable is x+6=4, then the other one of the linear equations of one variable is ()

A． x-6＝-4　B． x-6＝4

C. x+6＝4 D. x+6=-4

3. (4 points) The solution to the quadratic equation (x-2)2=9 is ()

A． x1=5, x2=-1 B. x1=-5, x2=1

C. x1=11, x2=-7 D. x1＝-1, x2＝7

4. (4 points) Fill in the blanks:

(1)x2-18x+________=(x-________)2;

(2)x2+x+________=(x+________)2.

【Error-prone Inventory】

[Example] Use the combination method to solve the equation x2-6x-1=0.

[Incorrect solution] By moving the terms, we get x2-6x=1; using the formula, we get x2-6x+(-3)2=1, that is, (x-3)2=1; taking the square root, we get x-3=±1; solution We get x1=4, x2=2.

[Error Cause Analysis] When formulating, half the square of the coefficient of the linear term should be added to both sides of the equation at the same time. The wrong solution only adds half the square of the coefficient of the linear term to the left side of the equation, but ignores that the square of half the coefficient of the linear term should also be added to the right side of the equation. The same number as above.

【correct】

16． (8 points) The height h and time t of an object thrown vertically follow the relationship formula

h=v0t-1/2gt2, where the acceleration of gravity g=10 m/s2, after the firecracker is ignited,

When the speed of v0=20 m/s rises, how long does it take for the firecracker to be 15 m above the ground?

17． (10 points) Explain: No matter what value a takes, the equation about x (a2-8a+20)x2+2ax+1=0 is a quadratic equation of one variable.

∵a2-8a+20=(a-4)2+4, no matter a takes any real number, (a-4)2≥0,

∴(a-4)2+4>0, that is, a2-8a+20≠0,

Therefore, no matter a takes any real number, the equation is a quadratic equation of one variable.

Keywords: Teaching courseware for solving quadratic equations with methods, Hebei Education Edition 9th grade mathematics PPT courseware download, 9th grade mathematics slide courseware download, Solving quadratic equations with methods PPT courseware download, .PPT format;

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Update Time: 2024-09-01

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

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