Question

What are the x-intercepts of the function below?

g(x)=(4x−1)(x+2)


(1 point)
Responses

(1, 0) and (2, 0)
(1, 0) and (2, 0)

(0.25, 0) and (-2, 0)
(0.25, 0) and (-2, 0)

(-0.25, 0) and (2, 0)
(-0.25, 0) and (2, 0)

(-1, 0) and (2, 0)

Answer 1

To find the x-intercepts of the function \( g(x) = (4x - 1)(x + 2) \), you need to set the function equal to zero and solve for \( x \):

\[
(4x - 1)(x + 2) = 0
\]

This equation will be satisfied when either of the factors is equal to zero.

1. Set the first factor to zero:
\[
4x - 1 = 0
\]
\[
4x = 1 \implies x = \frac{1}{4} = 0.25
\]

2. Set the second factor to zero:
\[
x + 2 = 0
\]
\[
x = -2
\]

Therefore, the x-intercepts are \( (0.25, 0) \) and \( (-2, 0) \).

The correct response is:
**(0.25, 0) and (-2, 0)**