It is known that the vertex of the parabola y = AX2 + BX + C (0 < 2A < b) is p (x0, Y0) It is known that the vertex of the parabola y = AX2 + BX + C (0 ＜ 2A ＜ b) is p (x0, Y0), and points a (1, ya), B (0, Yb) and C (- 1, YC) are on the parabola If Y0 ≥ 0 is constant, then The minimum value of yayb YC yA/(yB-yC)

3 ya=a+b+c yb=c yc=a-b+c
c>=b^2/4a
So ya / (Yb YC) = a + B + C / B-A > (a + B + B ^ 2 / 4A) / (B-A)
Let B / a = m > 2
We can get (2 + m) ^ 2 / 4 (m-1)
When m = 4, the minimum value is 3
Here B = 4A

The vertex of y = AX2 + BX + C (0 ＜ 2A ＜ b) is known to be p (x0, Y0). The vertex of y = AX2 + BX + C (0 ＜ 2A ＜ b) is known to be p (x0, Y0)
）The points a (1, ya), B (0, Yb), C (- 1, YC) are on the parabola
If Y0 ≥ 0 is constant, then
Minimum value of yayb YC. Ya / (Yb YC)
ya=a+b+c yb=c yc=a-b+c
c>=b^2/4a
So ya / (Yb YC) = a + B + C / B-A > (a + B + B ^ 2 / 4A) / (B-A)
Let B / a = m > 2
We can get (2 + m) ^ 2 / 4 (m-1)
When m = 4, the minimum value is 3
Here B = 4A
Who can help me explain this solution? If you can let me understand, I will double the score

Ya = a + B + C Yb = C YC = A-B + C (this step is to bring in x = - 1,0,1 respectively) C > = B ^ 2 / 4A (the vertex ordinate is C-B ^ 2 / 4A, which is greater than or equal to 0 according to the meaning of the problem) so ya / (Yb YC) = a + B + C / B-A > (a + B + B ^ 2 / 4A) / (B-A) (that is, bring in C) divides a by the square of a, and let B / a = m > 2

It is known that the vertex of the parabola y = ax ^ 2 + BX + C (o < 2A < b) is p (x0, Y0), the points a (1, ya), B (0, Yb), and C (- 1, YC) are on the parabola
We know that the vertex of the parabola y = ax ^ 2 + BX + C (o < 2A < b) is p (x0, Y0), the points a (1, ya), B (0, Yb), C (- 1, YC) are on the parabola
(1) When a = 1, B = 4, C = 10, find the coordinates of vertex p; find the value of Ya / Yb YC
(2) When yo ≥ 0 is constant, the maximum value of Ya / Yb YC is obtained

1. Take a = 1, B = 4, C = 10 into the analytic expression of the function to get y = x & # 178; + 4x + 10
A (1,15), B (0,10) C (- 1,7), B (0,10) C (- 1,7), B (0,10) C (- 1,7), a (1,15), B (0,10) C (- 1,7), B (0,10) C (- 1,7), B (0,10) C (- 1,
That is, Ya = 15, Yb = 10, YC = 7
So ya / Yb YC = 15 / 10-7 = - 5.5
two
Ya / (Yb YC)

The first term of an is a, the common ratio is Q, and Sn is the sum of the first n terms. Find S1 + S2 +... + SN

Sn=a(1-q^n)/(1-q),
So S1 + S2 +... + Sn = a (1-Q + 1-Q ^ 2 +...) +1-q^n)/(1-q)
=a[n-(q+q^2+…… +q^n)]/(1-q)
Because of Q + Q ^ 2 + +Q ^ n = q (1-Q ^ n) / (1-Q),
So S1 + S2 +... + Sn = a [n-q (1-Q ^ n) / (1-Q)] / (1-Q)
=a[n-nq-q-q^(n+1)]/(1-q)^2

Cut the largest circle out of a rectangular sheet of iron 76.5cm long and 32cm wide. What's the area of the circle

32 is the diameter of the circle
32 △ 2 = 16 (CM) 16x16 = 256 (cm 2)
A: the area of this circle is 256 square centimeters

Calculation: - 16 + 23 + (- 17) - (- 7)

The original formula = - 16 + 23-17 + 7 = - 33 + 30 = - 3

If a set of data x1, X2, X3 The variance of XN is 2, then a new set of data 2x1, 2x2, 2x3 The variance of 2xn is ()

To decorate a living room, you need 500 pieces of square bricks with a side length of 12 decimeters, and how many pieces of square bricks with a side length of 4 decimeters

500X12X12÷4X4=4500

Given x, y ∈ R +, 2x + 5Y = 10, find the maximum value of XY and the corresponding value of X, y

2x+5y=10,y = (10 - 2x)/5
xy = x(10 - 2x)/5 = -2x²/5+ 2x = (-2/5)(x² -5x)
= (-2/5)[(x- 5/2)² - 25/4]
= (-2/5)(x - 5/2)² + 5/2
When x = 5 / 2 (where y = 1), XY takes the maximum value of 5 / 2

When x belongs to (2 / π, 2 / 3 π), the inverse function of the function y = 1-sinx / 1 + SiNx is

y=(1-sinx)/(1+sinx)
1-sinx=y+ysinx
1-y=(1+y)sinx
sinx=(1-y)/(1+y)
x=arcsin((1-y)/(1+y))
Because arcsinx is in (- π / 2, π / 2)
So the inverse function is y = arcsin ((1-x) / (1 + x)) + π