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"Understanding quadratic equations of one variable" Quadratic equations PPT courseware 4
1. Review and review
For a quadratic equation of one variable
(1)(8-2x)(5-2x)=18 That is: 2x2-13x+11=0;
(2)(x+6)2+72=102 That is: x2+12x-15=0,
Can you find the x's in the equation separately?
2. Situation introduction
(1) There is a 100m long wire with a plastic cover on the outside. For some reason, there is a break in the middle. I will give you a multimeter (which can measure whether there is a break) to check. How can you quickly find the break? Communicate with peers.
(2) The length of the rectangular floor of the kindergarten activity classroom is 8 meters and the width is 5 meters. Now we are going to lay a carpet with an area of 18m2 in the middle of the floor. The width of the uncarpeted strip area around it is the same. Can you find Exceed this width?
For the equation (8-2x)(5-2x)=18, that is, 2x2-13x+11=0
(1) Based on the known conditions of the topic, can you determine the approximate range of x? Tell me your reasons.
(2) Is it possible that x is less than 0? Is it possible that x is greater than 4? Is it possible that it is greater than 2.5? Tell us your reasons and communicate with your peers.
(3) Complete the following table:
(4) Do you know what the required width x(m) is? Are there other solutions? Communicate with your peers.
Steps to solve quadratic equations of one variable using the idea of "pinch":
① Exclude some values from the value range of the unknown number x;
② Exclude again based on the specific circumstances listed in the question;
③List tables that can reflect the values of unknowns and equations for re-screening;
④Finally obtain the minimum value range or specific data of the unknown number.
In the problem of the previous lesson, the sliding distance x (m) of the bottom of the ladder satisfies the equation (x+6)2+72 =102. This equation can be transformed into a general form as x2+12x-15=0
(1) Can you guess the approximate range of sliding distance x(m)?
(2) Xiao Ming believes that the bottom has also slid by 1 m. Is his statement correct? Why?
(3) Could the sliding distance at the bottom be 2 m? Could it be 3 m? Why?
(4) What is the integer part of x? What is the tenth place?
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For more information about the PPT courseware "Quadratic Equations of One Variable and Understanding Quadratic Equations of One Variable", please click the "Quadratic Equations of One Variable Equations ppt Understanding Quadratic Equations of One Variable" ppt tag.
"Understanding quadratic equations of one variable" Quadratic equations PPT courseware 3:
"Understanding Quadratic Equations" Quadratic Equations PPT Courseware 3 The length of the rectangular floor of the kindergarten activity classroom is 8 meters and the width is 5 meters. Now we are going to lay a carpet with an area of 18m2 in the middle of the floor. There will be no carpet around it. The width of the strip areas are all the same. Observe...
"Understanding quadratic equations of one variable" Quadratic equations PPT courseware 2:
"Understanding Quadratic Equations" Quadratic Equations PPT Courseware 2 Review and Thinking Can you make certain decisions based on the sales profits of goods? Like linear equations and fractional equations, quadratic equations are also an effective way to describe the real world. mathematical model. ..
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"Understanding Quadratic Equations" PPT Courseware for Quadratic Equations Question 1 A carpet surrounded by lace of equal width is as shown below. Its length is 8m and its width is 5m. If the area of the rectangular pattern in the center of the carpet is 18m2, how wide is the lace? Solution: If the lace...