How to determine coefficient ABC according to quadratic function image For example, y = AX2 + BX + C let you compare the two algebraic expressions 2A + B and 2a-b, which are greater than 0 or less than 0 respectively. How to adjust? We know that a < 0, b > 0, C < 0 The axis of symmetry is to the left of x = 1 and to the right of 0

This generally depends on the position relationship between the axis of symmetry and x = 1
Because the axis of symmetry x = - B / 2A
If - B / 2A > 1, combined with a
Given the function f (x) = loga (1 + x), G (x) = ioga (1-x), where (a > 0 and a ≠ 1), let H (x) = f (x) - G (x)
(1) Judge the parity of H (x) and explain the reason
(2) If f (3) = 2, find the set of X with H (x) > 0
(1) H (x) = log a [(1 + x) / (1-x)]; domain (- 1,1)
h(-x)=loga[(1-x）/(1+x)]=-loga[(1+x)/(1-x）]=-h(x)
So, H (x) is an odd function
(2) From loga (1 + 3) = 2, a = 2 is obtained
So h (x) = log 2 [(1 + x) / (1-x)]; domain (- 1,1)
From H (x) > 0, (1 + x) / (1-x) > 1 can be obtained,
Simplification, that is, 2x (x-1)
How does ABC make image in quadratic function?
I remember a > 0 opening up, a < 0 opening down But what does B C > and 0 determine the image?
The larger a is, the smaller the opening is, the smaller C is the intersection point with y axis, and the ratio of B to a is the left-right translation of tube symmetry axis
B or C alone greater than or less than 0 itself does not have much significance, only when it is with a can it show their significance.
For example, the axis of symmetry x = - B / 2a, a and B jointly determine the left and right of the axis of symmetry.
The product of the two is C / A. the two determined by them are on the same side or the opposite side of the x-axis.
Given the function f (x) = loga (2 + x) - loga (2-x), when x ∈ [- 1,1], the set of function values of function f (x)
（1）0
f(x)=loga(2+x)/(2-x)
A the scope is not given
How to judge the value of quadratic function. ABC
Given a = {x | x ^ 2-2x-3 ＜ 0}, B = {x | loga (x-1) ＞ 0} (a ＞ 0, a ≠ 1), u = R, find (CUA) ∩ B
From the title,
Known set a = {x | x ^ 2-2x-3 ＜ 0}
So, a = (- 1,3)
Set B = {x | loga (x-1) > 0} (a > 0, a ≠ 1)
So,
Zero
(x-3)(x+1)
Quadratic function image through (0, - 1), (1,1) (2,4) three points, find their expressions
Given the set u = R, a = {x | x ^ 2 + y ^ 2 / 4 = 1}, B = {y | y = x + 1, X belongs to a}, then (CUA) ∩ (cub) = online, etc., please give the detailed process
First find out a, a is the range of X on the ellipse, that is [- 1,1]
B is [0,2]
CuA=(-∞,-1)∪(1,∞)
CuB=(-∞,0)∪(2,∞)
So (CUA) ∩ (cub) = (- ∞, - 1) ∪ (2, ∞)
Explain the idea of solving problems
When a diver performs 10m platform diving training, his body (as a point) is a parabola passing through the origin under the coordinate system as shown in the figure (the data marked in the figure are known conditions). When he jumps a specified action, under normal circumstances, the highest point in the air is 4 m away from the water surface and the water entry point is 4 m away from the pool. At the same time, before the height of 5 m away from the water surface, the diver's body (as a point) is a parabola, It is necessary to complete the required somersault and adjust the water entry posture, otherwise mistakes will occur
(1) Find the analytical expression of this parabola
(1) In the given rectangular coordinate system, let the highest point be a, the water entry point be B, and the analytical formula of parabola be a
According to the meaning of the title, the coordinates of point o are (0,0), the coordinates of point B are (2, - 10), and the ordinate of vertex A is 2 / 3
C=0
Square of 4ac-b = 2 / 3
4a+2b+c=-10
A1=-25/6 A2=-3/2
B1=10/3 B2=-2
C1 = 0 or C2 = 0
The symmetry axis of the parabola is on the right side of the y-axis, so - B / 2A > 0,
∵a＜0,∴b＞0,
∴a=-25/6,b=10/3,c=0,
The analytical formula of parabola is
Y = - 25 / 6x square + 10 / 3x
The system of equations c = 0
Square of 4ac-b = 2 / 3
4a+2b+c=-10
Let y = ax + BX + C cross the point (2, - 10)
When x = 2, y = - 10
So y = a * 2 + 2B + C = 4A + 2B + C = - 10
Let u = {1,2,3,4,5,6,7,8}, a = {2,4,6}, B = {3,4,5}, find a set B, a ∪ B, CUA, cub
A set B = {4}
A∪B={2,3,4,5,6}
CuA={1,3.5,7,8}
CuB={1,2,6,7,8}
What is a set B???? I don't think so
A∪B={2,3,4,5,6}
CuA={1,3,5,7,8}
CuB={1,2,6,7,8}
So simple, a ∪ B = {2 3 4 5 6}, CUA = {1 3 5 7 8}
Cub = {1 2 6 7 8} (U removes the remaining elements of B)
A∪B={2,3,4,5,6} CuA={1,3,5,7,8} CuB={1,2,6,7,8}
A∩B={4}
A∪B={2,3,4,5,6}
CuA={1,3,5,7,8}
CuB={1,2,6,7,8}

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