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"Using the Combination Method to Solve Quadratic Equations of One Variable" PPT Courseware 3 for Quadratic Equations of One Variable
Review and Thoughts
1. Use the direct square root method to solve the following equations
(1) x²-6=0
(2) (x+3)²=5
2. What are the characteristics of a quadratic equation of one variable that can be solved by the direct square root method?
Discuss
How to solve the equation: x²+6x+4=0?
(1) Observation: What is the relationship between (x+3)²=5 and this equation?
(2) Can you transform the equation into the form (x+h)²=k (k ≥ 0)?
Match the left side of the quadratic equation into a perfect square, and then use the direct square root method to solve it. This method of solving the quadratic equation is called the matching method.
When formulating, add half the square of the coefficient of the linear term to both sides of the equation.
Summarize
Steps to solve quadratic equations of one variable using the formula method:
Shifting terms: Move the constant term to the right side of the equation;
Recipe: Add half the square of the coefficient of the linear term to both sides of the equation, and make the left side of the equation a perfect square.
Square root: According to the meaning of square root, the square root of both sides of the equation;
Solution: Solve linear equations of one variable;
Definite solution: Write the solution to the original equation.
Summarize
1. Matching method: Like this, the left side of the equation is matched into a perfect square form containing x, and the right side is a non-negative number, so that the direct square root method can be used to solve the equation. This is the matching method.
2. Steps to solve quadratic equations of one variable using the combination method:
①Move items ②Chemify 1 ③Formula ④Decrease ⑤Definite solution
Change the original equation into the form of (x+h)2=k (where h and k are constants).
When k≥0, take the square root of both sides at the same time, so that the original equation is transformed into two linear equations of one variable.
When k<0, what about the solution of the original equation?
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"Using the Combination Method to Solve Quadratic Equations of One Variable" PPT courseware 2:
"Using the Combination Method to Solve Quadratic Equations" PPT Courseware 2 Review and review the steps of using the combination method to solve quadratic equations: 1. Move terms: move the constant term to the right side of the equation; 2. Formula: add both sides of the equation The square of half the coefficient of a linear term; 3. Square root: According to the square root meaning...
"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...
"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..