Question

What is the midpoint of the x-intercepts of f(x) = (x - 2)(x - 4)?

(-3, 0)
(-1, 0)
(1, 0)
(3, 0)​

Answer 1

(3, 0)​

Explanation:

The x-intercepts are the values of x that make f(x) be zero. They are ...

x = 2 . . . . makes the first factor zero

x = 4 . . . . makes the second factor zero

The midpoint is the average of these two values, ...

x = (2 +4)/2 = 3

The value of f(x) is 0 there, so the coordinate pair is (x, y) = (3, 0).

Answer 2

(3, 0)​

Explanation:

f(x) = (x - 2)(x - 4)

Using the zero product property

x-2 = 0 x-4 = 0

x=2 x=4

Are the x intercepts

The midpoint is (2+4)/2 = 6/2 = 3