Question

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

a) (-3, 0)
b) (-1, 0)
c) (1, 0)
d) (3, 0)

Answer 1

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

Step-by-step explanation:

To find the x-intercepts of the quadratic function f(x) = (x-2)(x-4), we set the function equal to zero and solve for x:

(x-2)(x-4) = 0

Simplifying, we get:

x-2 = 0 or x-4 = 0

So, x = 2 or x = 4. These are the x-intercepts of the function. To find the midpoint of these x-intercepts, we take the average of the two values:

(2 + 4)/2 = 6/2 = 3

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