Question

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

Answer 1

Well, we know that the x-intercepts are (0,2) and (0,4).  That means that the midpoint is just (0,3)

You can also use the midpoint formula:

$M=( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

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Answer 2

Answer:

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

Step-by-step explanation:

The given function is

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

To find the x-intercepts equation f(x) equals to 0.

$f(x)=0$

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

Using zero product property, equate each factor equals to 0.

$x-2=0\Rightarrow x=2$

$x-4=0\Rightarrow x=4$

The x-intercepts are (2,0) and (4,0). The midpoint of x-intercepts of f(x) is

$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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

$Midpoint=(3,0)$

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