In the second chapter, quadratic functions, equations and inequalities!

This one is deepened on the basis of junior high school mathematics. It is no longer the classic formula or formula for calculating values ​​in junior high school. Instead, it is combined with parabola, converting quadratic functions and equations into parabolas, and combining equations with parabola graphs.

One of the key points of this part is to understand the properties of equality and inequality, basic inequalities, quadratic functions and quadratic equations, and inequalities. Many boundary conditions will be given here, such as the value range of x between 0 and 12.

time, let you find the value range of the quadratic function f(x).

Or give you a rectangular area to plant flowers, give you the length of a railing, tell you how much larger the area of ​​​​the giant area surrounding the city is, and ask you to find the side length of this giant. This is to combine a quadratic function with an inequality, like this

For this type of question, there are often two values ​​obtained. As a result, one value is a negative value and must be removed, because the side length will not take a negative value.

The focus of this chapter is actually the drawing of quadratic functions of one variable. Whether you are good at learning or not depends on whether you are good at drawing!

Fortunately, Liu Yichen has a little talent in painting. His drawings are fast and beautiful, ten times better than his handwriting.

For a parabola of a quadratic function like this, draw the x and y coordinate axes, and then determine the situation of △. For example, if △>0, there are two foci with the x axis. The minimum value of the parabola is below the x circle, and the y value

Less than o. △=0, then there is only one intersection point between the parabola and the x-axis, and the minimum y value is 0. △<0, then there is no intersection point between the parabola and the x-axis, which means that when the equation is equal to 0, there is no real root, and then

Regardless of whether the x value is positive or negative, the value of the quadratic function is greater than 0, that is, the solution set is r, and the solution set less than 0 is the empty set?!

The essence of this chapter is actually the combination of functions and graphs. If you master it, you will be invincible. The speed of solving questions depends on how many questions you have answered. No matter how many questions you have answered, if you understand one question correctly, other questions will be better.

It's hard to get it wrong.

Unknowingly, Liu Yichen had already read Chapter 3. Chapter 3 is about the concept and properties of functions. This chapter is a more obvious watershed from junior high school. This is function, and function also runs through the entire high school mathematics.

, whether it is compulsory or elective, functions are always a hurdle that cannot be avoided. I don’t know how many people have died on functions. Those who cannot get a passing score in the high school mathematics exam can basically be said to have failed the function, resulting in confusion in subsequent studies.

Ignorant and half-informed.

Liu Yichen read this chapter slowly. He felt that he did not master the first two chapters 100%, but at least 90%. For the other chapters, if he listened to the teacher during the course, he would probably not have a problem with 100% mastering. But this third chapter

Chapter 1 must be treated with caution, because in high school mathematics compulsory course 1, Chapter 3, Chapter 4, and Chapter 5 are interlocking. In Chapter 3, functions are introduced, the depth of the function is increased, and power functions are introduced.

Chapter 4 adds exponential functions and logarithmic functions, and Chapter 5 adds trigonometric functions, plus the quadratic functions of Chapter 2. In essence, it is just a function.

As you can imagine, the entire high school mathematics compulsory textbook 1 boils down to just that - functions!

Whether you can get off to a good start in high school mathematics depends on whether the function can pass the test! How you perform in high school mathematics also depends on the function!

Unconsciously, time passed quietly and the bell rang. Only then did Liu Yichen know that there was going to be class in the afternoon. He quickly put his math textbook into his schoolbag, then picked up his schoolbag and ran towards the classroom.

Fortunately, the classroom of Grade 18 is two classrooms away from the library. Liu Yichen arrived at the classroom first and sat at his desk before Teacher Lin walked into the classroom!

Phew~!

so close!

Liu Yichen thought to himself.

If you are the first one in the class to be late for class, your efforts in changing Teacher Lin's impression of you in the morning will be in vain, and you will be listed as a disobedient child by Teacher Lin and irritate students.

In the last life, Teacher Lin had a very good impression of him and praised him in various ways. Later, he even wanted to connect him with her daughter. Unfortunately, Teacher Lin's daughter was 5 years younger than Liu Yichen. Liu Yichen was ashamed of the despicable behavior of an old cow eating young grass. At that time,

When he saw the fresh and tender flower of Sister Milk Tea being picked by Brother Dong, he was so angry that he jumped up and down.

Of course, the most important thing is that Teacher Lin’s daughter is so ugly!

"Everyone, please get ready. Bring your chairs and gather in the playground in 30 minutes. The opening ceremony will be held on the playground in the afternoon!" Teacher Lin said.

On the first day of school, there were actually no classes, and no other teachers appeared in front of the students. Only Teacher Lin, the Chinese teacher and class teacher, was doing the work on the first day of school.

The only thing to be done in the afternoon is the opening ceremony!

In Liu Yichen's opinion, this opening ceremony was very boring. The entire opening ceremony lasted about two and a half hours, with various leaders giving speeches and student representatives admonishing students. In Liu Yichen's eyes, this was like a lazy woman's foot wrap - long and smelly.

!

Liu Yichen looked at the corner of his system interface. Among the 100 hours of library study in task 3, 2/100 had appeared, which meant that he had completed the 2 hours of library study task at noon.

Liu Yichen thought again that after two hours of studying, he still had the fifth and final chapter of trigonometric functions in his high school mathematics compulsory course 1. He always felt itchy if he didn't finish it.

Terrible obsession!

Liu Yichen picked up the high school mathematics compulsory course 1 textbook and opened Chapter 5. Regarding the trigonometric function, one of the introduction points of the trigonometric function is the circle, the center of the circle, and the points on the two arcs. This gives us the angle α and the arc length l.

and the constituted area s, from which the arbitrary angle and radian systems are introduced, thus opening up the content of this chapter. The four quadrants are also introduced through the rectangular coordinate system, and the previous sets and inequalities are integrated.

As well as the conversion of angles and radians, the images and properties of trigonometric functions. These trigonometric functions are not limited to mathematics at this moment, but are also crucial to physics at this moment. For example, mechanical waves, light waves, etc. that will be learned in physics later will be applied.

Trigonometric functions to evaluate.

Liu Yichen took out a coin from his pocket, then drew a rectangular coordinate system on the draft paper, and then rolled the coin on the coordinate system to deepen his understanding and memory. With the memory in his mind, Liu Yichen also did not have a teacher to teach him.

You can learn by yourself, or review is more appropriate!

"Liu Yichen, everyone is discussing, why don't you join the discussion? What are you drawing?" Deng Linghao, who was sitting in front of Liu Yichen, saw Liu Yichen drawing on the paper, drawing an unknown figure, and said in confusion.

.

Teacher Lin said that in 30 minutes everyone would take chairs to the playground and leave after the opening ceremony. Without Teacher Lin as the head teacher, everyone naturally started chatting. Although most people had not known each other before, communication is human

It’s an instinct to communicate with classmates and then spread, not to mention that some of them are in the same dormitory and got to know each other yesterday.

"You little brat, what do you know? This is called a trigonometric function and this is a sine curve! Leave me alone!" Liu Yichen didn't even raise his head. Although these classmates were all high school classmates in the previous life, because this semester is over, they will

They are divided into liberal arts classes according to students' wishes, which means that everyone has been classmates for one semester, so they are not familiar with each other.

Deng Linghao is the one he is most familiar with in the class. It is simple that he is a relative of Mr. Deng. The two of them grew up together and fought countless times when they were young.

"You... forget it if you don't want to play, we won't play with you either!" Deng Linghao said angrily, then turned around and ignored Liu Yichen.

Liu Yichen curled his lips, you bastards, you know what it means that every inch of time is worth an inch of gold, an inch of gold cannot buy an inch of time, it is really shameful to waste time.

Chatting with you, how is it different from fishing at work?

"In the life of a top student, you always cherish time! When it comes to friendship, books are the best friends!" Liu Yichen thought with disdain.

The life of top academics is always lonely, and their real friends are books!

It’s so cold at high places!

Even though Liu Yichen is not yet a top student, it does not prevent him from becoming a top student mentally!

Studying math textbooks in the library at noon made Liu Yichen realize that in addition to the not-so-reliable Xueba system, his cheating device was also his cheating device through time travel and rebirth. Even though a lot of knowledge had been returned to the teacher, he had to re-learn and

It's two different things to not understand new learning at all. He learns at an incredibly fast speed. This kind of learning is simply a review for the third year of high school.

Unconsciously, it has arrived at 3:00. At this time, the afternoon sun is not so poisonous, which also means that the theme of the afternoon, the "Opening Ceremony", has officially arrived.

As the squad leader, Lin Ningwei took the class committee and began to direct everyone, leaving the classroom one by one, and heading to the playground under the leadership of the deputy squad leader.

Obviously, having been the monitor of the junior high school class for many years, and then serving as the class committee member of the high school class, he became more comfortable and played the real role of a monitor.

Among the girls in the class, Lin Ningwei is considered a beauty, and boys almost always blush when they look at her. Although she looks carefree, her body is honest and obeys her.

Liu Yichen also took the chair to the playground. Their chairs were all benches, which were enough for two people to sit. Liu Yichen came to the playground with his schoolbag and the bench, and sat in the last row of the class in order. After taking a quick look, he felt

This is where no one should be paying attention.

After two and a half hours of nonsense, Liu Yichen would not shamefully waste these two and a half hours. He directly abandoned the noise from the outside world and immersed himself in the world of trigonometric functions, from the classic sine function to y=asin(wxψ)

Graphing is also a combination of functions and graphs, and it also has a high demand for graphing. If you don’t graph and just think about it, 99% of students will be fools. Only when you are particularly proficient and have truly mastered it can you do it.
Chapter completed!