If the graph of the linear function y = (2a-3) x + A + 2 is above the x-axis in the section of - 2 ≤ x ≤ 1, then the value range of a is______ . | Math enthusiast | Mathematical art

If the graph of the linear function y = (2a-3) x + A + 2 is above the x-axis in the section of - 2 ≤ x ≤ 1, then the value range of a is______ .

Because y = (2a-3) x + A + 2 is a function of order one,
So 2a-3 ≠ 0, a ≠ 3
2，
When 2a-3 > 0, y increases with the increase of X. from x = - 2, y = - 4A + 6 + A + 2,
According to the graph of the function above the x-axis, there is - 4A + 6 + A + 2 > 0,
The solution is: 3
2＜a＜8
3．
When 2a-3 is less than 0, y decreases with the increase of X. from x = 1, y = 2a-3 + A + 2 is obtained. According to the graph of the function above the x-axis,
Then: 2a-3 + A + 2 > 0, the solution is: 1
3＜a＜3
2．
So the answer is: 1
3＜a＜8
3 and a ≠ 3
2．

If the graph of the linear function y = (2a-3) x + A + 2 is above the x-axis in the section of - 2 ≤ x ≤ 1, then the value range of a is______ .

Given that the function f (x) = x * 2 - (2a-1) x + A * 2-2 has at least one intersection point with the nonnegative semiaxis of X, the value range of a is calculated

That is, the equation x ^ 2 - (2a-1) x + A ^ 2-2 = 0 has at least one nonnegative solution
If the equation has only one solution
Then the discriminant = (2a-1) ^ 2-4 (a ^ 2-2) = 0
-4a+1+8=0
a=9/4
x^2-7/2x+49/16=0
X = 7 / 4 〉 0
If the equation has two different solutions
Then the discriminant is greater than 0, - 4A + 9 > 0, a

Given that a is the third quadrant angle, try to determine the final edge position of 2a and 0.5A And express them with sets

A is between 2K π + π and 2K π + 3 π / 2, so 2a is between 2K π and 2K π + π, which is the first or second quadrant angle. A / 2 between K π + π / 2 and K π + 3 π / 4 is the second or fourth quadrant angle

Given that a is the fourth quadrant angle, determine the position of the final edge of each corner in the following example: (1) a / 2 (2) a / 3 (3) 2A

(1) A / 2 in the second and fourth quadrants (2) a / 3 in the second and third and fourth quadrants (3) 2a in the third and fourth quadrants

Given that a is the third quadrant angle, how to determine the final edge position of 2a and 0.5A by drawing

If the final edge of 2a is in the first quadrant or the second quadrant 0.5A, you divide each quadrant into two parts, that is, you now have eight regions (in meter shape), and now from the X axis

If a is the angle of the third quadrant, then the quadrant where a / 2 is located is

In the second or fourth quadrant, the solution is as follows:
Because α is the third quadrant angle, so that 2K Wu + Wu < α < 2K Wu + 3 / 2 Wu,
If K is odd, then α is in the fourth quadrant,
If K is even, then α is in the second quadrant,

A is the second quadrant angle and a / 3 is the second quadrant angle

a[π/2+2kπ,π+2kπ]
a/3[π/6+2kπ/3,π/3+2kπ/3]
Then a / 3 is the first, second and fourth quadrant angles
When k = 0, a / 3 is the first quadrant angle,
When k = 1, a / 3 is the second quadrant angle,
When k = 2, a / 3 is the fourth quadrant angle,

Given that a is the angle of the third quadrant, find the quadrant where a third of a is located

∵ A is the angle of the third quadrant, i.e. 180 ° < a < 270 °
The angle of a third of a is: 60 ° < A / 3 < 90 °, that is, in the first quadrant

The point m (a, A-3) is a point on the bisector of the second and fourth quadrants It's going to be right now. Hurry up, OK~

The point m (a, A-3) is a point on the bisector of the second and fourth quadrants
Second, the bisector of the fourth quadrant is y = - X;
∴a-3=-a;
2a=3;
∴a=3/2;
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If the graph of the linear function y = (2a-3) x + A + 2 is above the x-axis in the section of - 2 ≤ x ≤ 1, then the value range of a is______ .