Question

Determine the x-intercept(s) of the function that translates the original function f(x)=x2
down 4 units.(1 point)
Responses

There are no x-intercepts.
There are no x -intercepts.

x=−16
and x=16
x equals negative 3.464 and x equals 3.464

x=−2
and x=2
x equals negative 2 and x equals 2

x=−4
and x=4

Answer 1

To find the x-intercept(s) of the function that translates the original function \( f(x) = x^2 \) down 4 units, we first need to determine the new function after the translation.

The original function is:
\[
f(x) = x^2
\]

Translating it down by 4 units gives:
\[
g(x) = f(x) - 4 = x^2 - 4
\]

Next, we find the x-intercepts of the function \( g(x) \) by setting it equal to zero:
\[
g(x) = 0 \implies x^2 - 4 = 0
\]

This can be factored:
\[
(x - 2)(x + 2) = 0
\]

Setting each factor to zero gives:
\[
x - 2 = 0 \quad \text{or} \quad x + 2 = 0
\]
\[
x = 2 \quad \text{or} \quad x = -2
\]

Thus, the x-intercepts of the function \( g(x) = x^2 - 4 \) are:
\[
x = -2 \quad \text{and} \quad x = 2
\]

The correct response is:
**x = -2 and x = 2**.