Given that the quadratic function y = ax ^ 2-4x + A-1 has a maximum value of 2, then the value of a is?

Given that the quadratic function y = ax ^ 2-4x + A-1 has a maximum value of 2, then the value of a is?

Function has a maximum value, indicating that the opening of the parabola is downward

If the maximum value of the quadratic function y = ax 2 + 4x + C is 3, then a= a=-1

If a quadratic function has a maximum value, then a

The image of the known quadratic function y = ax ^ 2-4x + C passes through point a (- 1,0) and point B (3, - 9)

Given that the image of the quadratic function y = ax-4x + C passes through a and B, the expression of the quadratic function is obtained
Y = ax ^ - 4x + C substituting (- 1,0), (3, - 9)
0=a+4+c
-9=9a-12+c
a=7/8
c=36/7
y=7/8x^-4x+36/7

Given the quadratic function f (x) = x ^ 2 + ax + B, a = {x | f (x) = 2x} = {2}, try to find the value of F (- 2)?

X ^ 2 + ax + B = 2x has equal roots 2. So a = - 2, B = 4
So f (- 2) = 4

Given the function y = x? + ax + B, a = {x ▏ x? + ax + B = 2x} = {2}, try to find the values of a and B and the analytic formula of quadratic function y

Set a has only one element 2, and the equation x 2 + ax + B = 2x has two equal real roots x = 2
x²+(a-2)x+b=0
X = 2 substitution
4+2(a-2)+b=0
2a+b=0
b=-2a
Discriminant = 0
(a-2)²-4b=0
a²-4a+4-4b=0
B = - 2A
a²+4a+4=0
(a+2)²=0
a=-2
b=-2a=4
The analytic formula of the function is y = x? - 2x + 4

Given the quadratic function f (x) = x ^ 2 ax B, a = {x | f (x) = 2x} = {22}, try to find the analytic solution of F (x)? The above question is wrong, and this is the right one Given the quadratic function f (x) = x ^ 2 + ax + B, a = {x | f (x) = 2x} = {22}, try to find the analytic solution of F (x)?

Because a = {x │ f (x) = 2x} = {22}
There is only one element, so the equation x ^ 2 + ax + B = 2x has only one
Discriminant based on roots
(a-2)^2-4b=0
b=(a-2)^2/4
So the equation is x ^ 2 + ax + (A-2) ^ 2 / 4 = 2x
Because x = 22 is the solution of this equation
Therefore, 22 ^ 2 + 22a + (A-2) ^ 2 / 4 = 44
1936+88a+a^2-4a+4=176
a^2+84a+1764=0
(a+42)^2=0
a=-42,b=484
So the function analytic formula of F (x) is y = x ^ 2-42x + 484

Given that the definition domain of quadratic function f (x) = ax ^ 2-2x + A + B is [0,3], and the range of value is [1,5], find the values of a and B To answer in detail, quick

In the case of (x), there are three kinds of definitions
(1) F (x) increases monotonically in [0,3]
Then f (0) = 1; f (3) = 5; a = 10 / 9; b = - 1 / 9
In this case, the symmetry axis of function f (x) is x = 9 / 10; obviously, f (x) is not monotonically increasing in [0,3]
It is in contradiction with the hypothesis, so let it go
(2) F (x) decreases monotonically in [0,3]
Then f (0) = 5; f (3) = 1; a = 2 / 9; b = 43 / 9
In this case, the symmetry axis of function f (x) is x = 9 / 2; obviously, f (x) is monotonically decreasing in [0,3]
Consistent with the hypothesis
(3) F (x) is not a monotone function in [0,3], that is, the symmetry axis of F (x) x = 1 / A is between [0,3]
Then 0 < 1 / a < 3; a > 1 / 3
At this time, f (x) decreases monotonically at [0,1 / a] and increases monotonically at [1 / A, 3]
F (1 / a) = 1, f (0) = 5; or F (1 / a) = 1, f (3) = 5;
1) If f (1 / a) = 1, f (0) = 5;
It is found that a = 1 / 4, B = 19 / 4, which is inconsistent with the assumption a > 1 / 3
2) If f (1 / a) = 1, f (3) = 5;
It is found that a = 1 / 3, B = 23 / 3, which is inconsistent with the assumption a > 1 / 3
Or a = 1, B = 1; it is consistent with the hypothesis, so it is reserved
To sum up, a = 2 / 9, B = 43 / 9 or a = 1, B = 1 are positive solutions

We know the inequality about X 2x-a > = - 3, x > = - 1, a value

2x-a≥-3
The result is as follows:
2x≥a-3
So:
x≥(a-3)/2
According to the meaning of the Title X ≥ - 1, we get: (A-3) / 2 = - 1;
a-3=-2
a=3-2
a=1.

If the solution sets of inequality (A-1) x < A + 5 and 2x < 4 are the same, then the value of a is () A. 7 B. 8 C. 9 D. 10

From 2x < 4, we can see that x < 2;
(1) When a > 1, (A-1) x < A + 5 can be converted into: x < A + 5
a−1，
∴a+5
a−1=2，
The solution is: a = 7;
(2) When a < 1, (A-1) x < A + 5 can be converted into: x > A + 5
a−1，
It doesn't agree with the meaning of the title
In conclusion, a = 7;
Therefore, a

We know that the inequality system about X is x-m ≥ n, 2x-m

x-m≥n,==>x≥n+m
2x-mx