The x-coordinate of the vertex is precisely halfway between the given roots 2 and 4; thus, x = (2+4)/2, or x=3. The y-coordinate is the value of the function at this x=3.
We can actually determine the equation of this quadratic from the zeros:
f(x) = (x-2)(x-4), or f(x) = x^2 - 6x + 8. To find the y-coord. of the vertex,, subst. 3 for x in f(x) = x^2 - 6x + 8: f(3) = 3^2 - 6(3) + 8 = 9 - 18 + 8, or -1. Then we know that the vertex is at (3, -1).
