"Using the Combination Method to Solve Quadratic Equations of One Variable" PPT Courseware 2

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"Using the Combination Method to Solve Quadratic Equations of One Variable" PPT Courseware 2

Review and review

Steps to solve quadratic equations of one variable using the formula method:

1. Move the term: Move the constant term to the right side of the equation;

2. Formula: Add half the square of the coefficient of the linear term to both sides of the equation;

3. Square root: According to the meaning of square root, the square root of both sides of the equation;

4. Solve: Solve linear equations of one variable;

5. Definite solution: Write the solution of the original equation.

Example 2 Solve the equation 3x²+8x-3=0.

1. Change to 1: Change the coefficient of the quadratic term to 1;

2. Move the term: Move the constant term to the right side of the equation;

3. Recipe: Add half the square of the coefficient of the linear term to both sides of the equation;

4. Deformation: Factor the left side of the equation and combine similar terms on the right side;

5. Square root: According to the meaning of square root, the square root of both sides of the equation;

6. Solve: Solve linear equations of one variable;

7. Definite solution: Write the solution of the original equation.

Turn on wisdom

Do it

A small ball pops up vertically with an initial velocity of 15m/s. Its height h(m) in the air and time t(s) satisfy the relationship: h=15t-5t².

When will the ball reach a height of 10m?

What old knowledge have been reviewed in this lesson?

Let’s continue asking two “old friends” to help out and deepen their understanding and application of the “matching method”:

The meaning of square root:

Perfectly square method: The formula a²±2ab+b² is called a perfectly square method, and a²±2ab+b² = (a±b)².

What new knowledge did you learn in this lesson?

Steps to use the compound method to solve a quadratic equation of one variable whose coefficient of the quadratic term is not 1:

1. Transform to 1: Change the coefficient of the quadratic term to 1 (divide both sides of the equation by the coefficient of the quadratic term);

2. Move the term: Move the constant term to the right side of the equation;

3. Recipe: Add half the square of the absolute value of the coefficient of the linear term to both sides of the equation;

4. Deformation: factorize the left side of the equation and combine similar factors on the right side;

5. Square root: According to the meaning of square root, the square root of both sides of the equation;

6. Solve: Solve linear equations of one variable;

7. Definite solution: Write the solution of the original equation.

Use the model of quadratic equations to answer or solve some problems in life (i.e., list quadratic equations to solve word problems).

Use the formula method to solve the following equations.

1. 4x² - 12x - 1 = 0;

2. 3x² + 2x – 3 = 0;

3. 2x² + x – 6 = 0;

4. 4x²+4x+10 =1-8x.

5. 3x² - 9x +2 = 0;

6. 2x² +6=7x;

7. x² – x +56 = 0;

8. -3x²+22x-24=0.

According to the meaning of the question, list the equations:

1. There is such a poem in an ancient Indian arithmetic book: "A group of monkeys were divided into two teams, happily playing games. One-eighth of them were then squared, jumping around in the woods; the other twelve were chirping, smart, lively and naughty. Tell me what the total number is?”

Solution: Suppose there are x monkeys in total. According to the question, we get

(1/8x)²+12=x

That is x² - 64x+768 = 0.

Solving this equation, we get

x1＝48;

x2=16.

2. Solve the following equations:

(1).6x² -7x+ 1 = 0;

(2).5x² -9x –18=0;

(3).4x² –3x =52;

(4).5x² =4-2x.

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"Using the Combination Method to Solve Quadratic Equations of One Variable" PPT courseware:

"Using the Combination Method to Solve Quadratic Equations" PPT courseware learning objectives: 1. Be able to use the combination method to solve quadratic equations whose quadratic term coefficients are not 1. 2. Experience exploring the general form of quadratic equations (x+h)=k (k0) process, further understand the meaning of the matching method 3. Experience...

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"Using the Combination Method to Solve Quadratic Equations of One Variable" Quadratic Equations PPT Courseware 3 Review and Thoughts 1. Use the direct square root method to solve the following equations (1) x-6=0 (2) (x+3)=5 2. Can What are the characteristics of quadratic equations of one variable solved by the direct square root method? Discuss one by one...

"Using the Combination Method to Solve Quadratic Equations of One Variable" PPT courseware for quadratic equations of one variable 2:

"Using the Combination Method to Solve Quadratic Equations" Quadratic Equations PPT Courseware 2 Review of Old Knowledge 1. What is the general form of the quadratic equation of X? 2. What are the integral equations you have learned? How are they solved? Remove denominators, remove brackets, move items, merge similar items..

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Update Time: 2024-10-03

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