This problem, entitle that synthesis of quadratic function, involves the solution of quadratic function, linear resolution function, isosceles triangle property, axisymmetric property, midpoint coordinate formula, and the solution of intersection coordinates of two functions by using undetermined coefficient method. The key to solve this problem is to use the combination of numbers and shapes, classified discussion and equation thought.

The following is an image of the answer/exercise/math /798383 parabola y = ax 2+bx+c (a ≠ 0) passing through point M(-2, root number 3), and the vertex coordinate is N(- 1, (4 times root number 3)/3), which intersects with the X axis at point A.

(1) Find the analytical formula of parabola;

(2) Point P is the moving point on the parabola symmetry axis. When △PBC is an isosceles triangle, find the coordinates of point P;

(3) Is there a point Q on the straight line AC to minimize the perimeter of △QBM? If it exists, find out the coordinates of Q point; If it does not exist, please explain why. If I can help you, I hope it can be adopted ~ Come on ~