When x = 3, the minimum value of y = - 1, and the image is over (0,7), the analytic expression of quadratic function about X is obtained

When x = 3, the minimum value of y = - 1, and the image is over (0,7), the analytic expression of quadratic function about X is obtained

Therefore, the analytic expression of quadratic function can be set as follows:
Y = a * (x-3) ^ 2-1, where a is greater than 0
And then there are:
7 = a * (0-3) ^ 2-1
A = 8 / 9
The analytic expression of this quadratic function is as follows:
y=8*(x-3)^2/9-1

It is known that the image of a quadratic function passes through points (0, - 2), and when x = 1, the function has a minimum value of - 3. (1) find the analytic expression of the quadratic function; (2) if the points (- 2, Y1), (1, Y2) and (3, Y3) are all on the image of the function, try to compare the sizes of Y1, Y2 and Y3

(1) Let the analytic formula of quadratic function be y = a (x-1) 2-3, since the parabola passes through the point (0, - 2), then a (0-1) 2-3 = - 2, and the solution is a = 1; therefore, the analytic formula of parabola is y = (x-1) 2-3. (2) ∵ a = 1 ﹥ 0, so the opening of throwing object line is upward; ∵ the symmetry axis of parabola is x = 1, ∵ (1, Y2) is parabolic Since (- 2, Y1) and (4, Y1) are symmetrical about the axis of symmetry, the size of Y1 and Y3 can be compared by comparing (4, Y1) and (3, Y3). Since there is an increasing function on the right side of the y-axis, Y1 > Y3. Then Y2 < Y3 < Y1

If the image of a quadratic function is known to pass through a point (2,7), and x = - 2 has a minimum value of - 1, then the analytic expression of the quadratic function is

When x = - 2, there is a minimum value of - 1,
Let this quadratic function be
Y = a (x + 2) & #178; - 1, and a (2 + 2) & #178; - 1 = 7, 16a = 8, a = 1 / 2
The analytic expression of this quadratic function is
y=1/2(x+2)²-1
That is y = 1 / 2x & # 178; + 2x + 1

Answers to the first volume of the ninth grade of Jiangsu Education Press

Exercise (1)
In the same circle or the same circle, the equal center angles are equal to the arcs and the same chords
In the same circle or equal circle, if two arcs are equal, then the central angle they are opposite_________ . the right string_______ ；
In the same circle or equal circle, if two strings are equal, then the central angle they are opposite_________ . opposite arc_______ ；

All are equal. You can draw a picture if you don't believe it

Who can give some exercises of attributive clauses? I'm in junior high school now
If it's good, I have a big reward!
There are a lot of questions with "who, who", which is my weakest point! I went to junior high school only with the answers of "that, who, which, who, who"

1、The people ( ) you were talking to are Russians.
A that B who C which D whom
The answer is a
That is often omitted as the object of the preposition to
Follow the verb, not before that
2、The man ( ) I saw is called Bob.
A whom B whose C who D which
The answer is C
Who is used as an object instead of who, which is often omitted
3、I'd like a room ( ) window looks out over the sea.
A that B which C whose D whom
The answer is C
"Who" can also be used as an attribute in a clause
4、This is the man ( ) I referred to.
A who B whose C whom D which
The answer is C
Who is used as the object of the preposition to, which follows the verb

Junior high school attributive clause exercises

1.The place _______ interested me most was the Children's Palace.
A. Which B. where C. what D. in which
3.This is the hotel _______ last month.
A. which they stayed B. at that they stayed
C. where they stayed at D. where they stayed
4.Do you know the year ______ the Chinese Communist Party was founded?
A. which B. that C. when D. on which
5.That is the day ______ I'll never forget.
A. which B. on which C. in which D. when
6.The factory ______ we'll visit next week is not far from here.
A. where B. to which C. which D. in which
8.This is one of the best films _______ .
A. that have been shown this year B. that have shown
C. that has been shown this year D. that you talked
9.Can you lend me the book ______ the other day?
A. about which you talked B. which you talked
C. about that you talked D. that you talked
10.The pen ______ he is writing is mine.
A. with which B. in which C. on which D. by which
11.They arrived at a farmhouse, in front of ______ sat a small boy.
A. whom B. who C. which D. that
12.The engineer ______ my father works is about 50 years old.
A. to whom B. on whom C. with which D. with whom
13.It there anyone in your class ______ family is in the country?
A. who B. who's C. which D. whose
14.I'm interested in ______ you have said.
A. all that B. all what C. that D. which
15.I want to use the same dictionary ______ was used yesterday.
A. which B. who C. what D. as
16.He isn't such a man ______ he used to be.
A. who B. whom C. that D. as
17.He is good at English, ______ we all know.
A. that B. as C. whom D. what
18.Li Ming, ______ to the concert enjoyed it very much.
A. I went with B. with whom I went C. with who I went D.I went with him
19.I don't like ______ as you read.
A. the novels B. the such novels C. such novels D. same novels
20.He talked a lot about things and persons ________ they remembered in the school.
A. which B. that C. whom D. what
21.The letter is from my sister, ______ is working in Beijing.
A. which B. that C. whom D. who
22.In our factory there are 2,000 workers, two thirds of ____ are women.
A. them B. which C. whom D. who
23.You're the only person ______ I've ever met ______ could do it.
A. who;/ B./; whom C. whom;/ D./; who
24.I lost a book, ______ I can't remember now.
A. whose title B. its title C. the title of it D. the title of that
25.Last summer we visited the West Lake, ______ Hangzhou is famous in the world.
A. for which B. for that C. in which D. what
26.I have bought such a watch _______ was advertised on TV.
A. that B. which C. as D. it
27.I can never forget the day _______ we worked together and the day ______ we spent together.
A. when; which B. which; when C. what; that D. on which; when
28.The way ______ he looks at problems is wrong.
A. which B. whose C. what D./
29.This is the reason ______ he didn't come to the meeting.
A. in which B. with which C. that D. for which
30.This machine, ______ for many years, is still working perfectly.
A. after which I have looked B. which I have looked after
C. that I have looked after D. I have looked after
31.The reason ______ he didn't come was ______ he was ill.
A. why; that B.that;why C. for that;that D.for which;what
32.He is working hard, ______ will make him pass the final exam.
A.that B.which C.for which D.who
33.That is not the way ______ I do it.
A./ B.which C.for which D.with which
34.I have two grammars, ______ are of great use.
A. all of which B. either of which C. both of that D. both of which
35.I want to use the same tools _______ used in your factory a few days ago.
A. as was B. which was C. as were D. which
36.My neigh bours used to give me a hand in time of trouble, _______ was very kind of them.
A. who B. which C. that D. it
37.This is the magazine _______ I copied the paragraph.
A. that B. which C. from that D. from which
38.He is not such a man _______ would leave his work half done.
A. that B. which C. who D. as
39. You can depend on whatever promise _______ he makes.
A. / B. why C. when D. whose
40. Smoking, _______ is a bad habit, is, however, popular.
A. that B. which C. it D. though
41. --- Did you ask the guard _______ happened?
--- Yes, he told me all _______ he knew.
A. what; that B. what; what C. which; which D. that; that
42. I shall never forget those years _______ I lived on the farm with
the farmers, _______ has a great effect on my life.
A. when; who B. that; which C. which; that D. when; which
43. The number of the people who _______ cars _______ increasing.
A. owns; are B. owns; is C. own; is D. own; are
44. During the days ________ , he worked as a servant at the Browns.
A. followed B. following C. to follow D. that followed
45. Is oxygen the only gas _______ helps fire burn?
A. that B. / C. which D. it
46. The clever boy made a hole in the wall, _______ he could see _____ was going on inside house.
A. which; what B. through which; what C. through that; what D. what; that
47. Is _______ some German friends visited last week?
A. this school B. this the school C. this school one D. this school where
48. John got beaten in the game, _______ had been expected.
A. as B. that C. what D. who
49. I have bought two ballpens, _______ writes well.
A. none of them B. neither of them C. neither of which D. none of which
50. All that can be eaten _______ eaten up.
A. are being B. has been C. had been D. have been
Reference answers and analysis
A. which is used as relative pronoun and subject in attributive clause
Do you know the man who I spoke to... Who is a relative pronoun and can be omitted as the object of preposition to
3. D. where is a relative adverb, which means place and is used as adverbial of place in attributive clause
4. C. when is a relative adverb, which means time and is used as adverbial of time in attributive clause
5. A. which is a relative pronoun and is the object of forget in clause
6. C. The analysis is the same as question 5
7. A. see question 3 for analysis
8. A. the antecedent of this sentence should be films. Therefore, the relative pronoun that is a negative number concept, and its predicate verb should use the repeated passive voice have been shown
Talk about sth.. About is a preposition, which should be used as the object, not that
10. A. with which is the structure of "preposition + relative pronoun", which is often used to guide the attributive clause. With has the meaning of "Yong", which can only be used after the preposition, not that. With which as an adverbial in the attributive clause, that is, he is writing with a pen
C. in front of which is in front of a farmhouse
12. D. with whom leads the attributive clause. With whom in the clause is my father works with the engineer
D. who leads the attributive clause and acts as the attributive of the subject family in the clause
14. A. that leads to attributive clause, because the antecedent is all
15. D. the same…… In this sentence, as is the subject of the clause
16. D. such……… As is a fixed usage. When as leads to attributive clause, it can be used as subject, object or predicative
17. B. as as a relative pronoun can be used alone to guide the non restrictive attributive clause. In this case, as does not refer to a noun in the subject sentence, but often refers to the meaning of the whole subject sentence. As can be used as the subject and object in the clause. The clause can be placed after or before the subject sentence. In this sentence, as is used as the object
18. B. Li Ming enjoyed it very much is the main clause, with whom I went to the concern is the attributive clause