The table of intervals would mean the interval where it is increasing, decreasing and so on right? If so, the key to finding that lies in finding the critical point of the function, which for a quadratic, is its vertex.
Now, the vertex can either be found out by differentiating (if you know calculus) or by using the formula -b/2a (x coordinate of vertex). Then, from the equation itself, you can determine if the vertex is a maxima or minima (if the coefficient of x^(2) is positive, the vertex is a minima and vice versa).
Knowing this, it can easily be inferred that if the vertex is a minima, for the range of values before the minima, the function is decreasing and for the range of values after, it is increasing. Vice versa for the maxima.