The x coordinate of the image vertex with y = x 2+2ax+3 =-a, and the function has the minimum value. For the minimum value in the world, it is necessary to compare the sizes of -a and 1 and 2.

When?

when-a & gt； When =2, the whole interval [1, 2] is to the left of -a, that is, the vertex of the image is not in the given interval. At this time, it is easy to know that the function is a subtraction function on [1, 2], so the function value is the smallest when x=2, so the minimum value is 4a+7.

When 1

-a^2+3