Question 2: How to learn math functions well in junior high school? Is there any good way? First, understand the connotation and essence of quadratic function.
The quadratic function Y = AX2+BX+C (A ≠ 0, A, B and C are constants) contains two variables X and Y. As long as we determine one of the variables first, we can find the other variable by analytical formula, that is, we can get a set of solutions. And a set of solutions is the coordinates of a point, in fact, the image of quadratic function is a graph composed of countless such points.
Familiar with the images and properties of several special quadratic functions.
1. Observe the shapes and positions of y=ax2, Y = AX2+K, Y = A (X+H) 2 images by tracing points, and get familiar with the basic features of their respective images. On the contrary, according to the characteristics of parabola, we can quickly determine which analytical formula it is.
2. Understand the translation formula of image "addition and subtraction, left plus right subtraction".
Y = AX2 → Y = A (X+H) 2+K "addition and subtraction" is K, and "adding left and subtracting right" is H. 。
In a word, if the coefficients of quadratic terms of two quadratic functions are the same, their parabolas have the same shape, but the translation of parabolas is essentially the translation of vertices because of their different coordinates and positions. If parabolas are in general form, they should be converted into vertices and then translated.
3. Through drawing and image translation, we understand and make it clear that the characteristics of analytical expressions are completely corresponding to the characteristics of images. When solving problems, we should have a picture in mind and see the function to reflect the basic characteristics of its image in our hearts.
4. On the basis of being familiar with the function image, through observing and analyzing the characteristics of parabola, we can understand the properties of quadratic function, such as increase and decrease, extreme value and so on. Distinguish the coefficients A, B, C, △ of quadratic function and the symbols of algebraic expressions composed of coefficients by images.
Third, we should make full use of the function of parabola "vertex".
1. We should be able to find the "vertex" accurately and flexibly. The form is y = a (x+h) 2+k → vertex (-h, k). For other forms of quadratic function, we can turn it into a vertex to find the vertex.
2. Understand the relationship between vertex, symmetry axis and maximum value of function. If the vertex is (-h, k) and the symmetry axis is x =-h, the maximum (minimum) value of y = k；; On the other hand, if the symmetry axis is x=m and the maximum value of y is n, then the vertex is (m, n); Understanding the relationship between them can achieve the effect of analyzing and solving problems.
3. Draw a sketch with vertices. In most cases, we only need to draw a sketch to help us analyze and solve problems. At this time, we can draw the approximate image of parabola according to the vertex and opening direction of parabola.
Understand and master the solution of the intersection of parabola and coordinate axis.
Generally speaking, the coordinates of a point consist of abscissa and ordinate. When we find the intersection of parabola and coordinate axis, we can give priority to one of the coordinates, and then find the other coordinate by analytical formula. If the equation has no real root, it means that the parabola and the X axis do not intersect.
From the process of finding the intersection point above, we can see that the essence of finding the intersection point is to solve the equation, which is related to the discriminant of the root of the equation, and the number of times the parabola intersects the X axis is determined by the discriminant of the root.
Quadratic functions are all parabolic functions (its function trajectory is like the trajectory of a ball, of course this is not important), so we can grasp the quadratic function by grasping its function image.
Pay attention to several points in the function image (standard formula y = ax 2+bx+c, a is not equal to 0):
1, the opening direction is related to the quadratic coefficient a, indicating that the opening is upward, and vice versa.
2. There must be an extreme point, which is also the maximum point. If the opening is upward, it is easy to imagine that this extreme point should be the minimum point, and vice versa. The abscissa of the extreme point is -b/2a. Extreme points are prone to application problems.
3. it doesn't necessarily intersect with the x axis. When the determinant δ of the root = B2-4ac0, there are two intersections, and the corresponding equation has two real number solutions.
4. Inequality. Clear the above three points, we can certainly solve the inequality of reference function image ...
Question 3: How to learn junior high school functions well? First of all, do you know what learning well is? Get high marks? The function of junior high school is the mathematical relationship between two quantities, and this relationship is the function. 1. linear function (including proportional function) y=kx+b, y = kx 2. Inverse proportional function y = k/x 3. Quadratic function Y = AX 2+BX+C Y changes with X. Generally, the senior high school entrance examination will form an answer according to the combination of function images and polygons (usually quadrangles and triangles). No skills, do more questions, think hard and sum up.
Question 4: How to learn functions well in junior high school! ! ! ! First of all, do you know what learning well is? Get high marks?
Function theory in junior high school is a mathematical relationship between two quantities, and this relationship is a function.
1. Linear function (including proportional function)
y=kx+b，y=kx
2. Inverse proportional function
y=k/x
3. Quadratic function
y=ax^2+bx+c
Generally, the relationship between y and x will be answered according to function images and polygons (generally regular quadrangles and triangles).
No skills, do more questions, think hard and sum up.
Question 5: What is the best way to learn functions in junior high school? First of all, do you know what it means to learn well? Get high marks?
The function of junior high school is the mathematical relationship between two quantities, and this relationship is the function.
1. Linear function (including proportional function)
y=kx+b，y=kx
2. Inverse proportional function
y=k/x
3. Quadratic function
y=ax^2+bx+c
Generally, the relationship between y and x will be answered according to function images and polygons (generally regular quadrangles and triangles).
No skills, do more questions, think hard and sum up.
Question 6: How can we learn quadratic function well? How to learn math well in senior two;
To truly understand the mathematical definition, don't be specious.
Cultivate logical thinking in solving problems and understand where to start.
Start with conditions: understand the function of conditions in the topic and its function, and quickly infer the conclusions and results that can be drawn from it. Then, combined with the parallel conditions, we can draw further conclusions and finally solve the problem.
Starting with the result: when the function of the condition cannot be determined, we can consider starting with the result. First of all, we should combine the unconditional part of the topic and think of the possible necessary conditions for reaching this conclusion. Then advance to the original conditions given by the topic and solve the problem.
(3) Cultivate good mathematical spirit
First of all, on the basis of the conclusion and answer, carefully understand the problem-solving process and whether you really know the conclusion. If you don't understand, don't be happy with the answer you got. You should answer or ask your teacher or classmate again. Every step is required to have a rigorous derivation basis, or a theorem or axiom, and it is never taken for granted. If you don't ask, this is very important for learning math. To cultivate good mathematical spirit, we must ask more questions.
< 4 > Choose a topic with moderate difficulty for self-training.
There are two requirements for the selection of exercises: breadth and longitude. According to the textbook knowledge and the content of the teacher's lecture, it is a good time-saving method to sum up the key points of study, listen to the teacher and watch the students do it. At the same time, it is required to take care of all the knowledge points learned and practice every knowledge point. If the knowledge points are relatively simple, you can choose exercises with relatively high difficulty. Correspondingly, if it is difficult, you can choose exercises with moderate difficulty. It is unnecessary and difficult, so practice more.
Classical exercises always contain more knowledge points, which requires the solvers to have strong comprehensive ability and mathematical thinking, and be good at using conditions. It's not very difficult, but it requires strong insight and decision-making ability, and at the same time, it promotes the conclusion conditions, and then meets somewhere to solve the problem.
〈5〉 Cultivate interest in mathematics
Don't think that math problems are scientists, and they only reach the level of teachers at most. Actually, it's not. Anyone should look at the whole world with suspicion. Don't doubt your different opinions. If you still have objections after your own judgment, you should bravely raise them, and don't give up your opinion because of one or two mistakes. This is not only the focus of solving problems, but also the focus of cultivating good living habits. There is no doubt that there is no innovation.
Many students are not interested in mathematics because they didn't do well in the exam, so they deny themselves and even give up mathematics. Therefore, we must have a correct view of examination. It's just a way for teachers and classmates to test their learning situation. Where they fail, they will stand up. Careless or not, it doesn't matter. Carelessness is generally due to the fact that good habits are not formed at ordinary times, so it is inevitable that the thinking is not concentrated during the exam and it is easy to answer without careful thinking. Another point is easier, as long as you spend more time reviewing, you can prevent it from happening again. As long as you develop good mathematical spirit and thinking, you can give full play to your skills in the exam.
Learning mathematics is not only learning to solve problems, but also learning to observe and improve life. Cultivate your observation ability and interest in life, and you will benefit endlessly in your later life. The future society needs talents who can solve problems, not nerds who can only solve problems. People who can only solve problems are always backward, not creative and not competitive.
Do more exercises and ask the teacher to have a good attitude.
Don't put too much pressure on yourself
You can also look at the review questions in high school.
Communicate with teachers and classmates more to increase interest in mathematics.
1. I don't deny that being good at math is related to genius, but being good at math is not a genius's patent.
2. Mathematics examines the sensitivity of reaction, which is what we usually call mathematical consciousness. We have to relate all the relevant knowledge points in an instant to do a good job. This is not only a difficult place to learn mathematics, but also its bright spot.
3. To learn math well, you must first ask yourself if you really want to learn it well. If you can really do this, then you have succeeded by one fifth.
4. Put it into practice. Where there is a will, there is a way. One hundred and twenty Qin passes will eventually return to Chu. If you work hard, you can swallow Wu with three thousand armour. " > >；
Question 7: How can we learn junior high school functions well? Is there any good way to remember the images of various functions? It is much easier to associate images with functions and remember them.
Question 8: What foundations do you need to learn junior middle school functions well? It will be solved in a few words.
1. Binary linear equation is a linear function. If x and y are expressed in a rectangular coordinate system, it is a straight line.
2. Binary quadratic equation is a quadratic function, and its image is a conic curve.
3.{y=X2+ 1
{Y=X+ 1 solution: no solution, 1 group solution, 2 groups solution.
4. Image of the above example:
A parabola intersects a straight line:
One intersection or two intersections?
Disjoint: there is no intersection (no solution)
5. The derivative of quadratic function is a linear function, which represents the rate of change of quadratic function (that is, the tangent of quadratic function at a certain point! ! ! The slope! ! ! )。 Let the derivative be equal to zero, and the value of x is the point of maximum or minimum.
When the first year of college is over!
Question 9: How to learn junior middle school functions? I have a poor functional foundation now. Is there any way? Function and number axis, ok? If you know the number axis, let y=kx+b first, then the intersection point between the image and the ordinate is b, and the edge of the angle between the image and the abscissa is the distance between the intersection point of the image and the origin point and the distance between the intersection point of the image and the origin point on the ordinate. According to that angle, k can be obtained by comparing neighbors. If the image is up, k is positive, otherwise, k is negative. Hope to adopt me ....