It is known that the shape and size of the image of the quadratic function y = a (x + m) &# 178; + k are the same as the parabola y = - 1 / 2 (x-4) &# 178, And the vertex of the image is just the intersection of the line y = 3 / 2X-4 and y = - 2x, so we can find the analytic expression of the quadratic function

It is known that the shape and size of the image of the quadratic function y = a (x + m) &# 178; + k are the same as the parabola y = - 1 / 2 (x-4) &# 178, And the vertex of the image is just the intersection of the line y = 3 / 2X-4 and y = - 2x, so we can find the analytic expression of the quadratic function

Solve the equations
y= 3/2 x-4
y=-2x
The result is: x = 8 / 7
y=-16/7
The vertex coordinates of the parabola are (8 / 7, - 16 / 7)
∴m=-8/7 ,k=-16/7
∵ the shape and size of the parabola are the same as that of y = - 1 / 2 (x-4) & # 178
∴IaI=I-1/2I
∴a=±1/2
The analytical formula of the parabola is as follows:
Y = 1 / 2 (x - 8 / 7) & # 178; - 16 / 7 or y = - 1 / 2 (x - 8. / 7) & # 178; - 16 / 7
I'm glad to solve the above problems for you. I hope it will be helpful to your study

There are two points (x1, Y1) (X2, Y2) on the parabola y = (x + m) & # + K, and the distance from (x1, Y1) to the straight line x = - M is 3,
The distance from (X2, Y2) to the straight line x = - M is 2. Which is bigger between Y1 and Y2? Why?

From y = (x + m) & # + K, we can know that the parabola is symmetric with respect to the straight line x = - m, the opening is upward, and the lowest point of the parabola is (- m, K)
If you draw a graph, you can see that with the increase of Y, the distance from the point on the parabola to x = - M increases, so Y1 > Y2