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"Understanding quadratic equations of one variable" Quadratic equations PPT courseware 2
Review and Thoughts
Can you make certain decisions based on product sales profits?
Like linear equations and fractional equations, quadratic equations are also an effective mathematical model that describes the real world.
The length of the rectangular floor in a kindergarten classroom is 8m and the width is 5m. Now we are going to lay a carpet with an area of 18m2 in the middle of the floor. The width of the surrounding uncarpeted strip areas is the same. Can you find this width?
Solution: If the required width is xm, then the length of the rectangular pattern in the center of the carpet is (8-2x) m and the width is (5-2x) m. According to the meaning of the question, the equation can be obtained: (8-2x) (5 -2x) =18. Can you simplify this equation?
Observe the following equation:
10²+11²+12²＝13²+14²
Can you find five other consecutive integers such that the sum of the squares of the first three numbers is equal to the sum of the squares of the last two numbers?
If the first number among five consecutive integers is x, then the following four numbers can be expressed as: ________, ________, ________, ________.
From the above three questions, we can get three equations:
(8-2x)(５-2x)=18;
x²+(x+1)²+(x+2)²=(x+3)²+(x+4)²
(x＋６)²+7²＝10²
What do the above three equations have in common?
The above equations are all integral equations containing only one unknown number x, and they can all be transformed into the form ax²+bx+c=0 (a, b, c are constants, a≠0). Such equations are called quadratic equations of one variable.
Let ax² + bx + c = 0 (a, b, c are constants, a≠0) called the general form of a quadratic equation of one variable, where ax², bx, c are called quadratic terms, linear terms and constant terms respectively, a, b are respectively They are called quadratic term coefficients and linear term coefficients.
Think about it:
1. The equation about x (k-3)x²+2x-1=0. When k≠3, it is a quadratic equation of one variable.
2. The equation about x (k²-1)x² + 2 (k-1) x + 2k + 2=0. When k≠±1, it is a quadratic equation of one variable. When k=-1, it is a linear equation of one variable.
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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 4:
"Understanding Quadratic Equations" Quadratic Equations PPT Courseware 4 1. Review Review For the quadratic equation (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 x in the equation separately? ..
"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" PPT courseware of quadratic equations of one variable:
"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...