what is the midpoint of the x - intercepts of $f(x)=(x - 2)(x - 4)$?\n(-3,0)\n(-1,0)\n(1,0)\n(3,0)
what is the midpoint of the x - intercepts of $f(x)=(x - 2)(x - 4)$?\n(-3,0)\n(-1,0)\n(1,0)\n(3,0)
Answer
Answer:
D. (3,0)
Explanation:
Step1: Find x - intercepts
Set (f(x)=0), so ((x - 2)(x - 4)=0). Then (x-2 = 0) or (x - 4=0), which gives (x=2) and (x = 4). The x - intercepts are the points ((2,0)) and ((4,0)).
Step2: Use mid - point formula
The mid - point formula for two points ((x_1,y_1)) and ((x_2,y_2)) is ((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})). Here (x_1=2,y_1 = 0,x_2=4,y_2 = 0). Substituting into the formula, we get ((\frac{2 + 4}{2},\frac{0+0}{2})=(3,0)).