The graph and Y-axis of the linear functions y = (m-2) x + 1 and y = (m-1) x + M & # 178; - 5 intersect point P and point Q respectively. If point P and point q are symmetric about x-axis, the value of M is obtained

The graph and Y-axis of the linear functions y = (m-2) x + 1 and y = (m-1) x + M & # 178; - 5 intersect point P and point Q respectively. If point P and point q are symmetric about x-axis, the value of M is obtained

Because y = (m-2) x + 1 when x = 0, y = 1
So the line goes through P (0,1)
And y = (m-1) x + M & # 178; - 5 when x = 0, y = M & # 178; - 5
So the line goes through Q (0, M & # 178; - 5)
Also p and Q are symmetric about X axis
So M & # 178; - 5 = - 1
m²=4
m=±2
When m = + 2, y = (m-2) x + 1 = 1
So m = - 2

In the same coordinate system, draw the image of the function Y1 = 2x ^ 2, y2 = 2 (X-2) ^ 2 and Y3 = 2 (x + 2) ^ 2, and explain the relationship between the image of Y2Y3 and the image of Y1 = 2x ^ 2

As shown in the figure, Y2 can be obtained by translating Y1 two units to the right, and Y3 can be obtained by translating Y1 two units to the left

Function Y1 = - 5x + 1 / 2. Y2 = 1 / 2x + 1, so that the value of the smallest integer x of Y1 < Y2 is

-5x+1/2-1
x>-1/11
The minimum integer is 0