In order to know that the quadratic function f (x) passes through the point (0,1) and satisfies the condition f (x + 1) - f (x) = 2x, the analytic expression of the function f (x) is obtained Please tell me if you know

In order to know that the quadratic function f (x) passes through the point (0,1) and satisfies the condition f (x + 1) - f (x) = 2x, the analytic expression of the function f (x) is obtained Please tell me if you know

Let f (x) = ax & sup2; + BX + C, then f (x + 1) - f (x) = a (x + 1) & sup2; + B (x + 1) + C - (AX & sup2; + BX + C) = 2aX + (a + B) = 2x. By comparison, we get 2A = 2A + B = 0, a = 1b = - 1. Because f (x) passes through the point (0,1), we get C = 1, so f (x) = x & S
The coefficient of quadratic term of quadratic function FX is a, and the solution set of inequality FX > - 2x is (1,3). If x ≤ - 1, FX + 5A
Solution: Let f (x) = ax ^ 2 + BX + C
f(x)>-2x
That is, the solution set of ax ^ 2 + (B + 2) x + C > 0 is (1,3), so there is a
Solution: Let f (x) = ax ^ 2 + BX + C
f(x)>-2x
That is, the solution set of ax ^ 2 + (B + 2) x + C > 0 is (1,3), so there is a
It is known that the coefficient of quadratic term of quadratic function f (x) is a, and the solution set of inequality f (x) > - 2x is (1,3). If the maximum value of F (x) is a positive number, then the value range of real number a is______ .
Let f (x) = AX2 + BX + C, (a < 0), the two roots of the equation f (x) = - 2x are 1, 3, that is, AX2 + (B + 2) x + C = 0, the two roots are 1, 3. The inequality a (A2 + 4A + 1) about a is obtained
It is known that the minimum value of quadratic function FX is 1 and F0 = F2 = 3
F0 = F2 = 3, indicating that the axis of symmetry x = (0 + 2) / 2 = 1
The minimum value of FX is 1
So let f (x) = a (x-1) ^ 2 + 1
Substituting f (0) = 3, 3 = a + 1, a = 2
So f (x) = 2 (x-1) ^ 2 + 1 = 2x ^ 2-4x + 3
Fo = F2 indicates that x = 1 is the axis of symmetry, i.e. the maximum value at fi is 1
f0=3
f1=a+b+c=1
f2=4a+2b+3=3,
It'll work out
If (A-2) x (absolute value of A-1) - 7 = 5 is a linear equation of one variable, then the square of - a minus 1 / a =
Is the title like this? (A-2) x ∣ A-1 ∣ - 7 = 5
If so, the solution is: if a is greater than 1, then the absolute value is A-1. If a is less than 1, then the absolute value is 1-A
The first case: (A-2) x (A-1) - 7 = 5
a2-3a+2-7=5
The solution is a = 5, a = - 2
If a = 5, then - A2 - 1 / a = 125-1 / 5 = 124 / 5
If a = - 2, then 4 + 1 / 2 = 4.5
Second case:
（a-2）*(1-a)-7=5
-a2 -3a-2-7=5
a2 +3a+14=0
The solution is a=
I have forgotten the universal formula
Factorization of 4x2y2 - (x2 + y2-z2) 2
The answer is (x + y + Z) (x + Y-Z) (X-Y + Z) (z-x + y). How do you get it?
(Note: there are brackets after the letter, the power is behind the letter, the letter is quadratic, and the 2 after the bracket also means quadratic.)
4x2y2-(x2+y2-z2)2=[2xy-(x2+y2-z2)][2xy+(x2+y2-z2)]=[z^2-(x-y)^2][(x+y)^2-z^2]=(z+x-y)(z-x+y)(x+y+z)(x+y-z)=x+y+z)(x+y-z)(x-y+z)(z-x+y)
The geometric meaning of constant C in quadratic function y = ax & # 178; + BX + C (a ≠ 0)
The geometric meaning of C in quadratic function is to play the role of up and down translation,
For example: y = ax & # 178; + BX + C (a ≠ 0) is compared with y = ax & # 178; + BX (a ≠ 0)
That is to translate y = ax & # 178; + BX up and down the absolute value of C into three units
When C > 0, it moves up
When C
x=0,y=c
The intersection coordinates of the function and the Y axis
Or the intercept on the y-axis.
Coordinate of intersection point of function and Y axis
It is known that the product of three rational numbers a, B and C is negative, and their sum is positive. When x = | a | / A + | B | / B + | C | / C, we can find the algebraic formula
The power of 2006X - 2006X!
a. The product of B and C is negative, indicating that there is one or three negative numbers in a, B and C
If their sum is positive, then there is only one negative number
Then x = 1
I can't understand what you said later. Is it 2006 * x ^ 2008 or (2006X) ^ 2008
3x-1 = 2x use the solution of one variable linear equation (write down the name of deformation)
3x-1=2x
3x-2x=1
X=1
First, move 2x to the left, then 3x minus 2x is equal to x, then the original formula is changed to x minus 1 is equal to 0, so x is equal to 1
Factorization (x2-1) (y2-1) - 4xy
Ask experts to help
=x²y²-x²-y²+1-4xy
=(x²y²-2xy+1)-(x²+2xy+y²)
=(xy-1)²-(x+y)²
=(xy-1+x+y)(xy-1-x-y)