Factorise.

Break Brakets

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.