Question

Help it's timed.

A function g(x) has x-intercepts at (StartFraction 1 Over 2 EndFraction, 0) and (6, 0). Which could be g(x)?


g(x) = 2(x + 1)(x + 6)

g(x) = (x – 6)(2x – 1)

g(x) = 2(x – 2)(x – 6)

g(x) = (x + 6)(x + 2)

Answer 1

Option 2.

Explanation:

We need to find a function g(x) which has x-intercepts at (1/2,0) and (6,0).

To find the x-intercepts substitute g(x)=0 in function.

For option 1,

`2(x + 1)(x + 6)=0`

Using zero product property we get

`(x + 1)=0` and
`(x + 6)=0`

`x=-1` and
`x=-6`

Therefore the x-intercepts of this function at (-1,0) and (-6,0).

For option 2,

`(x-6)(2x-1)=0`

Using zero product property we get

`x-6=0` and
`2x-1=0`

`x=6` and
`x=(1)/(2)`

Therefore the x-intercepts of this function at (1/2,0) and (6,0).

For option 3,

`2(x-2)(x-6)=0`

Using zero product property we get

`(x -2)=0` and
`(x -6)=0`

`x=2` and
`x=6`

Therefore the x-intercepts of this function at (2,0) and (6,0).

For option 4,

`(x + 6)(x + 2)=0`

Using zero product property we get

`(x +6)=0` and
`(x +2)=0`

`x=-6` and
`x=-2`

Therefore the x-intercepts of this function at (-2,0) and (-6,0).

Therefore, the correct option is 2.