Question

The zeros of a quadratic function are 2 and 4 what is the vertex of the function

Answer 1

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).