The image of y=- 1/2x+m passes through point A (-2,3) and is substituted into x=-2, so y= 1+m=3, so m=2.

So the straight line is y = (- 1/2) x+2, and further b (4 4,0) is obtained.

Substituting a and b into y=ax2+bx-2, we get A = 1/2 and B =-3/2.

The quadratic function is: y = x 2 (1/2)+(3x/2)-2.

Assuming that k units are translated along the positive direction of the Y axis, the new image is:

y - K = x^2 ( 1/2)+ (3x/2)-2

So: y = x 2 (1/2)+(3x/2)-2+k, and Q(0, k) can be obtained from the meaning of the question.

Because of PQ‖x axis, the ordinate of point P is also K.

For straight lines: y = (- 1/2) x+2, y=K, x=4-2K, so: P(4-2K, k).

Substitute the p coordinate into y = x 2 (1/2)+(3x/2)-2+k.

Solve a quadratic equation with one variable, K=4 or 3/2.