Formula of symmetry axis of function

Formula of symmetry axis of function

For quadratic function y = ax ^ 2 + BX + C, the axis of symmetry is: x = - B / 2A

The problem of symmetric axis and symmetric point of function (formula and conclusion)
Kneel down and ask for some
1. Function is symmetric about point (x, y)
2. Function on x = a symmetry
3. Function on y = B symmetry
Derivation and conclusion of the formula
College entrance examination can be applied, after the problem does not have to waste time

1. The symmetric function of Y1 = f (x1) with respect to point (x, y) is Y1 = 2y-f (2x-x1)
2. The symmetric function of Y1 = f (x1) with respect to x = a is Y1 = f (2a-x1)
3. The symmetric function of Y1 = f (x1) with respect to y = B is Y1 = 2b-f (x1)

How to look at the axis of symmetry of F (x + 2) = f (2-x), is there a fixed formula for finding the axis of symmetry

If f (x) satisfies f (a + x) = f (A-X), then x = a is the symmetry axis of the function image
If the function f (x) satisfies f (x) = f (2a-x), then x = a is the symmetry axis of the function image

Mathematical function problems often have expressions, what does this mean?

An expression is an analytic expression

Calculation by formula
1.〔（3a+b）（3a-b）〕²
2.（2x+y）²（2x-y）²
3.（5m+2n）²—（5m-2n）²
4.（-5x+3y-2z）²
5.（-a-b+3）²
6.（-3x-5y）²
7.（-2a+3b-5c）（-2a-3b+5c）
8.（3m-4n+2）（-3m-4n-2）
9. Given x + x 1 / 2 = 5, find the value of X & sup2; + X & sup2; 1 / 2
10. Given A-B = 7, ab = 2, find the value of a & sup2; + B & sup2
11. Given X & sup2; - 8x + Y & sup2; + 6y + 25 = 0, find the value of X and y

1.[（3a+b）（3a-b）]^2
=[(3a)^2 - b^2]^2
=(9a^2 - b^2)^2
=81a^4 - 18a^2b^2 + b^4
2.（2x+y)^2（2x-y)^2
=[(2x+y)(2x-y)]^2
=[(2x)^2 - y^2]^2
=(4x^2 - y^2)^2
=16x^4 - 8x^2y^2 + y^4
3.（5m+2n)^2 —（5m-2n)^2
=[(5m+2n)+(5m-2n)][(5m+2n)-(5m-2n)]
=(10m)(4n)
=40mn
4.（-5x+3y-2z)^2
=25x^2 - 15xy + 10xz - 15xy + 9y^2 - 6yz + 10xz - 6yz + 4z^2
=25x^2 - 30xy + 20xz + 9y^2 - 12yz + 4z^2
5.（-a-b+3)^2
=a^2 + ab - 3a + ab + b^2 - 3b - 3a - 3b + 9
=a^2 + 2ab - 6a + b^2 - 6b + 9
6.（-3x-5y）²
=9x^2 + 30xy + 25y^2
7.（-2a+3b-5c）（-2a-3b+5c）
=[-2a+(3b-5c)][-2a-(3b-5c)]
=(-2a)^2 - (3b-5c)^2
=4a^2 - 9b^2 + 30bc - 25c^2
8.（3m-4n+2）（-3m-4n-2）
=-(3m-4n+2)(3m+4n+2)
=-[(3m+2)-4n][(3m+2)+4n]
=-[(3m+2)^2 - (4n)^2]
=-9m^2 - 12m - 4 + 16n^2
9.[x+(1/x)]^2 = x^2 + 2 + (1/x)^2 = 25
x^2 + 1/x^2 = 25-2=23
10.a^2 + b^2 = (a-b)^2 - 2ab = 7^2 - 2×2=49-4=45
11.x^2-8x+y^2+6y+25=0
(x^2-8x+16)+(y^2+6y+9)=0
(x-4)^2 + (y+3)^2=0
∵ (x-4) ^ 2 and (y + 3) ^ 2 are constant ≥ 0
∴x-4=0 ,y+3=0
x=4 ,y=-3

Calculating a formula should belong to the class of mathematical function
Ten numbers are known
5、9、23、53、105、185、299、453、653、905、
Ask the great God to figure out what formula is used or what law is applied

X ^ 3 + 2 * x ^ 2 + X + 5. The above 10 numbers correspond to the values when x equals 0 to 9

A very simple math problem, high school winter vacation homework
(2) Represents the square of this number
Find the intersection circle equation of two circles x (2) + y (2) - 4x-6 = 0 and X (2) + y (2) - 4y-6 = 0 whose center is on the straight line X-Y-4 = 0

Because: X * 2 + y * 2-4x-6 = 0 and X * 2 + y * 2-4y-6 = 0 intersect with (3,3) and (- 1, - 1) let the center of the circle be (a, b), then: (x + a) * 2 + (y + b) * 2 = R * 2, take (3,3) and (- 1, - 1) into (3 + a) * 2 + (3 + b) * 2 = R * 2 (A-1) * 2 + (B-1) * 2 = R * 2, subtract up and down, and then use the square difference formula to get: (a + 3-A +

If f (x) is an increasing function defined on R, a (- 1, - 1) and B (2,1) are two points on its image, then the complement of the solution set of | f (x) | 1 is ()
A.（-1,2）
B.（1,4）
C.(-∞,-1）∪[4,＋∞]
D.(-∞,-1）∪[2,＋∞]

Choose D
Because f (x) is an increasing function, through a and B, we can draw | f (- 1) | = | f (2) | = 1
So the solution set of | f (x) | 1 is
Its complement is. (- ∞, - 1) ∪ [2, + ∞]

Sesame blossom edition was first printed by Jiangxi education press in December 2009
Don't fill in the blanks in the first edition of physics in December 2009

Classmate, I am also sesame blossom winter vacation homework
It was a lot of work
No one else can have sent it to you
I went online to find the process
You type the first few words
A question came out
It's easy to find
It took me two or three hours to write physics
Basically all the big questions have been found

The functional relationship between the selling price P yuan and the time t day of a commodity in the past 30 days is
P={ t+20 0
The image of the function f (x) = log (2) x is shifted 2 units to the left along the X axis to obtain the image of the function g (x).
(1) Write the domain of G (x)
(2) Solving inequality g (x) > 4

If the daily sales amount is y yuan, then y = P · Q
P={ -t^2+20t+800,0