The function y=-8x is a linear function.

The function y=4x+ 1 is a proportional function.

The opening of parabola y=-3(x-2)2-5 is downward.

The symmetry axis of parabola y=4(x-3)2- 10 is x=3.

Summary of junior high school mathematics knowledge points: plane rectangular coordinate system

The following is the study of the content of plane rectangular coordinate system. I hope students can master the following content well.

Cartesian coordinates/Cartesian coordinates

Plane Cartesian coordinate system: Draw two mutually perpendicular number axes with coincident origin on the plane to form a plane Cartesian coordinate system.

The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.

Elements of a plane rectangular coordinate system: ① On the same plane; ② Two axes of numbers are perpendicular to each other; ④ The origin coincides.

Three rules:

① The specified positive direction: the horizontal axis is right, and the vertical axis is oriented in the positive direction.

(2) the provisions of the unit length; Generally speaking, the unit length of the horizontal axis and the vertical axis is the same; In fact, sometimes it can be different, but it must be on the same axis.

③ Quadrant definition: the upper right is the first quadrant, the upper left is the second quadrant, the lower left is the third quadrant, and the lower right is the fourth quadrant.

I believe that the students have mastered the knowledge of plane rectangular coordinate system, and I hope they can all be admitted.

Knowledge points of junior high school mathematics: the composition of plane rectangular coordinate system

Let's learn about the composition of the plane rectangular coordinate system.

Composition of plane rectangular coordinate system

Two number axes perpendicular to each other on the same plane and having a common origin form a plane rectangular coordinate system, which is called rectangular coordinate system for short. Usually, the two number axes are placed in the horizontal position and the vertical position respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the X axis or Y axis is collectively called coordinate axis, and their common origin O is called the origin of rectangular coordinate system.

Through the explanation and study of the composition knowledge of plane rectangular coordinate system, I hope students can master the above contents well and study hard.

Junior high school mathematics knowledge points: the nature of the coordinates of points

The following is a study on the coordinate properties of points in mathematics. Students should take a closer look.

Properties of point coordinates

After the plane rectangular coordinate system is established, the coordinates of any point on the coordinate system plane can be determined. Conversely, for any coordinate, we can determine a point it represents on the coordinate plane.

For any point C on the plane, the intersection point C is perpendicular to the X-axis and Y-axis respectively, and the corresponding points A and B perpendicular to the X-axis and Y-axis are respectively called the abscissa and ordinate of the point C, and the ordered real number pairs (A, B) are called the coordinates of the point C. ..

A point is in different quadrants or coordinate axes, and its coordinates are different.

I hope that the students can master the knowledge of the above coordinate nature, and I believe that the students will achieve excellent results in the exam.

Knowledge points of junior high school mathematics: general steps of factorization

About the general steps of factorization in mathematics, we will explain the following knowledge.

General steps of factorization

If the polynomial has a common factor, first mention the common factor, if there is no common factor, consider using the formula method for the polynomial; If it is a polynomial with four or more terms,

Usually, the group decomposition method is used, and finally the cross multiplication factor is used to decompose the factors. So it can be summarized as "one mention", "two sets", "three groups" and "forty words".

Note: Factorization must be decomposed until each factor can no longer be decomposed, otherwise it is incomplete factorization. If the topic does not clearly indicate the scope of factorization, it should refer to factorization within rational numbers, so the result of factorization must be the product of several algebraic expressions.

I believe the students have mastered the general steps of factorization, and I hope they will do well in the exam.

Knowledge points of junior high school mathematics: factorization

The following is the knowledge explanation of factorization in mathematics. I hope the students will study hard.

factoring

Definition of factorization: transforming a polynomial into the product of several algebraic expressions is called factorization of this polynomial.

Factorizing elements: ① The result must be an algebraic expression ② The result must be a product ③ The result is an equation ④.

The relationship between factorization and algebraic expression multiplication: m(a+b+c)

Common factor: The common factor of each term of a polynomial is called the common factor of each term of this polynomial.

Determination of common factor: ① When the coefficient is an integer, take the greatest common factor of each term. The product of the greatest common divisor of the same letter and the lowest power of the same letter is the common factor of this polynomial.

To select a common factor:

① Determine the common factor. ② Determine the quotient formula ③ The common factor formula and the quotient formula are written in the form of product.

Factorizing attention;

(1) Lost letters are not allowed.

(2) It is not allowed to lose the same items. Please check the quantity of items.

③ Change the double brackets into single brackets.

(4) The results are arranged in the order of number, single letter and single polynomial.

⑤ The same factor is written as a power.

⑥ The first minus sign is placed outside the brackets.

⑦ Similar items in brackets are merged.

Through the above explanation and study of factorization content knowledge, I believe that students have mastered it very well, and I hope the above content will be helpful to students' learning.