Find the minimum value of F (x) = x & # 178; - 2aX + 2 in [- 1,1] 😊

Find the minimum value of F (x) = x & # 178; - 2aX + 2 in [- 1,1] 😊

Quadratic function y = (x-a) ^ 2 + 1-A ^ 2
If the opening is upward, it needs to be classified and discussed, and its axis of symmetry is x = A. because - 1 ≤ x ≤ 1,
(1) When m = - 1, we get the minimum value,
That is (- 1-A) ^ 2 + 1-A ^ 2 = 3 + 2A
(2) When - 1
This problem calls three values repeatedly;
f(-1)=3+2a
f(1)=3-2a
f(a)=2-a^2
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The opening of the parabola is upward, and the axis of symmetry is; X = a
When a
It is known that E1 and E2 are two non collinear vectors in the plane, a = 3e1-2e2, B = - 2E1 + E2, C = 7e1-4e2
C is represented by a and B
From a = 3e1-2e2, we can get: E1 = (a + 2e2) / 3. From b = - 2E1 + E2, we can get: E1 = (e2-b) / 2  (a + 2e2) / 3 = (e2-b) / 22a + 4e2 = 3e2-3be2 = - 3b-2a. Substituting E2 into a = 3e1-2e2, we can get a = 3E1 + 6B + 4ae1 = - a-2b  C = - 7a-14b + 12b + 8A = a-2b
c=a-2b
Let C = XA + Yb
Then the equations 3xe1-2ye1 = 7e1 and - 2xe2 + Ye2 = - 4e2 can be obtained
Find x = 1, y = - 2
So C = a-2b
What graph does the equation m (3x + 4Y-2) + n (2x + y + 2) = 0 represent?
Is it a straight line system passing through the intersection of L1: 3x + 4Y-2 = 0 and L2: 2x + y + 2 = 0? If so, what's the difference between (3x + 4Y-2) + λ (2x + y + 2) = 0?
The former represents all lines passing through the intersection of L1: 3x + 4Y-2 = 0 and L2: 2x + y + 2 = 0; the latter needs to remove L2
solution
The equation m (3x + 4Y-2) + n (2x + y + 2) = 0 is a linear system passing through the intersection of l1:3x + 4Y-2 = 0 and l2:2x + y + 2 = 0
And this (3x + 4Y-2) + λ (2x + y + 2) = 0 also represents the linear system of the intersection of l1:3x + 4Y-2 = 0 and l2:2x + y + 2 = 0
But there is one less line in this line system, 2x + y + 2 = 0. Can you explain why L2 is removed in the latter? Because no matter λ is any real number, the line (3x + 4Y-2) + λ (2x + y + 2... Expands
solution
The equation m (3x + 4Y-2) + n (2x + y + 2) = 0 is a linear system passing through the intersection of l1:3x + 4Y-2 = 0 and l2:2x + y + 2 = 0
And this (3x + 4Y-2) + λ (2x + y + 2) = 0 also represents the linear system of the intersection of l1:3x + 4Y-2 = 0 and l2:2x + y + 2 = 0
But this line system is short of a line 2x + y + 2 = 0?
Addition and subtraction of integral
Manager Li has a mobile phone and a PHS. When paying the phone bill in October, manager Li found that the cost of mobile phone is 1.8 times that of PHS. In order to control and reduce the phone bill, manager Li decided to take certain measures. It is estimated that the cost of mobile phone will be reduced by 40% in November and that of PHS will be increased by 30%. Do you think manager Li's measures are feasible? Explain the reasons
(1) Let October be PHS, the cost is x, and the cost of mobile phone is 1.8x;
(2) The total cost in October is x + 1.8x = 2.8x;
(3) In November, the cost of PHS is (1 + 0.3) x = 1.3x, and that of mobile phone is (1-0.4) * 1.8x = 1.08x;
(4) 083x = 1.382.381;
(5) 38x
Don't you know if you try? What can I ask you
Factorization: (y2-4y) (y2-4y + 1) - 6
Original formula = (y ^ 2-4y) ^ 2 + (y ^ 2-4y) - 6
=(y^2-4y+3)(y^2-4y-2)
=(y-1)(y-3)(y^2-4y-2)
Given that the function f (x) = x ^ 3 + ax ^ 2, x = 2 is an extreme point of F (x), find the maximum and minimum value of F (x) in the interval [- 1,3]
The derivative of the function is f '(x) = 3x ^ 2 + 2aX, which has the extreme value at x = 2, that is, f' (2) = 3 * 2 ^ 2 + 2A * 2 = 0, a = - 3, f (x) = x ^ 3-3x ^ 2F '' (x) = 6x-6, f '' (x) = 0 at x = 1, that is, the function has the maximum value at x = 1, in the interval [- 1,3], f (- 1) = - 4, f (3) = 0f (1) = - 2
It is known that E1 and E2 are two unit vectors with an angle of 60 ° and the angle between a = E1 + E2 and B = e1-2e2 is calculated
The answer is 120
Let the angle between a and B be x, then cos x = a * B / |a | 124; 124; 124; 124\\\124\124\\124\124\124\\124\\124\\\\\124\\\\\124\\\\\\\\\\\\\\\\\\\\socosx = (- 3 / 2) / 3 = - 1 / 2, so x = 120 degree
Using function image to solve 1.4x + 1 = 3x + 2 2.4x + 5 ＞ 03 {2x + y = 32x + 2Y = 5}
1、 Two straight lines y = 4x + 1 and y = 3x + 2 are drawn in the rectangular coordinate system. The abscissa X of the intersection is the solution of the equation;
2、 In the rectangular coordinate system, draw a straight line y = 4x + 5, the x value corresponding to the part above the X axis is the solution of the inequality;
3、 Two straight lines y = - 2x + 3 and y = - x + 5 / 2 are drawn in the rectangular coordinate system. The intersection coordinate (x,) is the solution of the equations
Xiao Zhang's income balance last year was 5000 yuan, which is estimated to be 8000 yuan this year. His income is 20% higher than that of last year, and his expenditure is 12% lower than that of last year
(1) If you spent a yuan last year, how much did you earn last year? How much did you earn and spend this year?
(2) If you spend a yuan this year, how much is your income this year? How much is your income and expenditure last year?
A classmate came across such a problem: A & sup2; - AB = 20, ab-b & sup2; = - 12, finding the values of the algebraic expressions a & sup2; - B & sup2; and a & sup2; - AB + B & sup2;, but he couldn't find the values of a and B. the students helped him to solve this problem
A student came across such a problem when he was working on the problem: A & sup2; - AB = 20, ab-b & sup2; = - 12, finding the values of the algebraic formula A & sup2; - B & sup2; and a & sup2; - 2Ab + B & sup2;, but he could not find the values of a and B, so the students helped him to solve the problem
Last year's income was 5000 + a yuan, this year's expenditure (1-12%) was a = 88% a income was 88% a + 800088% a + 8000 = (5000 + a) * (1 + 20%) 1.2a-0.88a = 8000-60000.32a = 2000a = 6250, last year's income was 11250 yuan. This year's income and expenditure were 13500 yuan and 5500 yuan respectively
How to decompose x ^ 2 + 4xy + 4Y ^ 2 + 4x + 8y + 4
x^2+4xy+4y^2+4x+8y+4
=(x+2y)^2+4(x+2y)+4
=(x+2y+2)^2
The square of (x + 2Y + 2)
(x+2y+2)^2
x^2+4xy+4y^2+4x+8y+4
=(x^2+4xy+4y^2)+4x+8y+4
=(x+2y)^2+4(x+2y)