Quadratics in Math 20-2
The vertex sits at x = -b/(2a), and the zeros come from factoring or from the quadratic formula.
A worked example
For y = x^2 - 2x - 8 the vertex x is -(-2)/2 = 1 and y = 1 - 2 - 8 = -9, so the vertex is (1, -9).
The mistake people actually make
A negative a makes the vertex a maximum, so the range is y ≤ q rather than y ≥ q. Check the discriminant before hunting for x-intercepts that do not exist.