x^2 - 5x + 6
(x - 2) (x - 3)
Intercepts x axis at x = 2 and x = 3
so intercepts twice.
whether its vertex lies above or below or on the x-axis
I would pick a number between 2 and 3 ie. 2.5 and subtitute into x^2 - 5x + 6
If its positive answer, its above x axis.
In this case its negative so its below.
Try the second one.
For the second one, x is not an integer.
Use the quadratic formula.