Question

Which equation, when graphed, has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16)?

f(x) = –(x – 2)(x – 4)
f(x) = –(x + 2)(x + 4)
f(x) = –2(x – 2)(x – 4)
f(x) = –2(x + 2)(x + 4)

Answer 1

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

if x=2 ⇒ f(x)=y=0 ⇒ graph of f(x) intercept x axis in (2,0)
if x=4 ⇒ f(x)=y=0 ⇒ graph of f(x) intercept x axis in (4,0)
if x=0 ⇒f(x)= -2 *(-2)*(-4)= - 16 ⇒ graph of f(x) intercept y axis in (0,- 16)

⇒ f(x)= -2 (x - 2) ( x - 4) is the answer

Answer 2

Answer:  The correct option is (C) $f(x)=-2(x-2)(x-4).$

Step-by-step explanation:  We are given to select the correct equation such that its graph has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16).

We know that the co-ordinates of the x-intercepts and the y-intercept will satisfy the equation.

So, we will check the given functions one by one.

Option (A) is

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

Here,

$f(2)=-(2-2)(2-4)=0,\\\\f(4)=-(4-2)(4-4)=0,\\\\f(0)=-(0-2)(0-4)=-8\neq -16.$

So, this option is not correct.

Option (B) is

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

Here,

$f(2)=-(2+2)(2+4)=-24\neq 0.$

So, this option is not correct.

Option (C) is

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

Here,

$f(2)=-2(2-2)(2-4)=0,\\\\f(4)=-2(4-2)(4-4)=0,\\\\f(0)=-2(0-2)(0-4)=-16.$

So, this option is correct.

Option (D) is

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

Here,

$f(2)=-2(2+2)(2+4)=-48\neq 0.$

So, this option is not correct.

Thus, The correct equation is $f(x)=-2(x-2)(x-4).$

Option (C) is correct.