Cycle 1. In a plane, a closed curve formed by a moving point rotating around a certain point with a certain length is called a circle. A circle has countless axes of symmetry.
2. Related characteristics of circles
(1) diameter
The line segment connecting the center of the circle and any point on the circle is called radius, and the letter is expressed as R.
The line segment passing through the center of the circle with both ends on the circle is called the diameter, and the letter is denoted as d.
A straight line with a diameter is the symmetry axis of a circle. In the same circle, the diameter of the circle is d=2r.
(2) Chords
A line segment connecting any two points on a circle is called a chord. The longest chord in the same circle is the diameter. A straight line with a diameter is the symmetry axis of a circle, so there are countless symmetry axes of a circle.
(3) Arc shape
The part between any two points on a circle is called an arc, which is represented by "⌒".
Fraction 1, algebraic expression a divided by algebraic expression b, if there is a denominator in division b, then this is a fraction. For any fraction, the denominator is not 0.
2. The numerator and denominator of the fraction are multiplied or divided by the same algebraic expression that is not equal to 0, and the value of the fraction remains unchanged.
Fractional operation 1, multiplication: take the product of molecular multiplication as the numerator of the product, and the product of denominator multiplication as the denominator of the product.
2. Division: dividing by a fraction is equal to multiplying the reciprocal of this fraction.
3. Addition and subtraction:
(1) Add and subtract fractions with the same denominator, and add and subtract molecules with the same denominator.
(2) Fractions with different denominators are divided into fractions with the same denominator first, and then added and subtracted.
Fractional equation 1, the equation with unknown number in denominator is called fractional equation.
2. The solution whose denominator is 0 is called the root increment of the original equation.
The quadratic equation with one variable has only one unknown, and the highest coefficient of the unknown term is 2.
The relationship between 1 and quadratic function of quadratic equation with one variable
Everyone has studied quadratic function and has a deep understanding of it, such as solution, representation in images and so on. In fact, the quadratic equation of one variable can also be expressed by quadratic function. In fact, the quadratic equation of one variable is also a special case of quadratic function, that is, when y is 0, it constitutes the quadratic equation of one variable. Then, if expressed in a plane rectangular coordinate system, the quadratic equation of one variable is the intersection of the X axis in the image and the quadratic function. This is the solution of the equation.
2. The solution of a quadratic equation
As we all know, a quadratic function has vertices (-b/2a, 4ac-b2/4a), which is a very important point for us to remember. As mentioned above, the quadratic equation with one variable is also a part of the quadratic function, so it also has its own solution, from which all solutions of the quadratic equation with one variable can be obtained.
(1) matching method
The equation is transformed into a complete square formula by using the formula and solved by direct Kaiping method.
(2) Factor decomposition method
Select the common factor, apply the formula, and cross multiply. The same is true for solving quadratic equations with one variable. Using this, the equation can be solved by several products.
(3) Formula method
This method can also be used as a general method to solve quadratic equations with one variable. The roots of the equation are x 1 = {-b+√ [B2-4ac]}/2a, and x2 = {-b-√ [B2-4ac]}/2a.
The above are the knowledge points of ninth grade mathematics that I compiled. I hope I can help you.