Question

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

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

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

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

x=−4 and x=4

Answer 1

To find the x-intercepts of the function that results from translating the original function \( f(x) = x^2 \) down 4 units, we first express the new function after the translation.

The new function after translating \( f(x) \) down 4 units is:

\[
g(x) = f(x) - 4 = x^2 - 4
\]

Next, to find the x-intercepts, we set \( g(x) = 0 \):

\[
x^2 - 4 = 0
\]

Now, we can solve for \( x \):

\[
x^2 = 4
\]

Taking the square root of both sides:

\[
x = 2 \quad \text{or} \quad x = -2
\]

Therefore, the x-intercepts of the function \( g(x) \) are:

\[
x = -2 \quad \text{and} \quad x = 2
\]

The correct response from the options provided is:

**x equals negative 2 and x equals 2**.