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

Solution:

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

We have to find the midpoint of the x-intercepts.

By midpoint formula, \([\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}]\)

Now, x - 2 = 0

⇒ x = 2

x - 4 = 0

⇒ x = 4

The x-intercepts are 2 and 4.

The coordinates are (2,0) and (4,0).

Midpoint = \([\frac{2+4}{2},\frac{0+0}{2}]\)

Midpoint = \([\frac{6}{2},0]\)

Midpoint = (3, 0)

Therefore, the midpoint of the x-intercepts is (3, 0).

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

Summary:

The midpoint of the x-intercepts of f(x) = (x - 2)(x - 4) is (3, 0).