Question

A function g(x) has x-intercepts at (1/2,0) 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

The answer is g(x)=(x-6)(2x-1).hope this helps please add brainlist

Answer 2

Answer:

$\boxed{g(x) = (x - 6)(2x - 1)}$

Step-by-step explanation:

An x-intercept is the value of x when g(x) = 0. So, for each function, we must set g(x) = 0 and solve for x.

(a) g(x) = 2(x + 1)(x +  6) = 0

x + 1 = 0     x + 6 = 0

    x = -1           x = -6

Wrong.

(b) g(x) = (x - 6)(2x - 1)

x - 6 = 0     2x – 1 = 0

    x = 6            2x = 1

                          x = ½

Right.

(c) g(x) = 2(x - 2)(x - 6)

x - 2 = 0     x - 6 = 0

    x = 2           x = 6

Wrong.

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

x + 6 = 0     x +2 = 0

    x = -6          x = -2

Wrong.

The only function that has x-intercepts at (½, 0) and (6, 0) is

$\boxed{g(x) = (x - 6)(2x - 1)}$