<image>Given that points P(a, 4) and Q(1, b) are symmetric with respect to the x-axis. 
(1) Find the values of a and b; 
(2) If \( y = ax^{2} + bx \), try to write the functional relationship between y and x; 
(3) Based on the functional relationship in (2), complete the following table:

(4) According to the results in (3), hypothesize what the minimum value of y is, and for what value of x this occurs?