Since you have asked all the questions, I will help you.

Solution: (1) Let the analytical formula of parabola be: y=a(x+3)(x-4), then there is:

4=a(0+3)(0-4)，a =- 1/3；

Therefore, the analytical formula of parabola is: y =-1/3 (x+3) (x-4) =-1/3x2+1/3x+4;

(2) According to (1), y =-1/3x2+1/3x4 =-1/3 (x-1/2) 2+49//kloc.

So the vertex coordinates of parabola are: (1/2,49/ 12), and the maximum value is 49/12;

(3) Easy to know OA=3, OB = OC = 4；;

Then AB=5, AC=7, CD = 2；;

Connect DQ, because BD divides PQ vertically, then DP=DQ, so:

∠PDB=∠QDB，

And AD=AB, get: ∠ABD=∠ADB,

So ∠QDB=∠ABD, get qd ‖ AB;

∴△CDQ∽△CAB has:

CD/CA=DQ/AB，2/7=DQ/5，

∴PD=DQ= 10/7，AP=AD-PD=5- 10/7= 25/7，

So t = 25/7.