Question

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
x equals negative 4 and x equals 4
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Answer 1

To determine the x-intercepts of the function that translates the original function \( f(x) = x^2 \) down 4 units, we first need to write the new function.

The function translated down 4 units is:
\[
f(x) = x^2 - 4
\]

Next, we find the x-intercepts by setting \( f(x) = 0 \):
\[
x^2 - 4 = 0
\]

We can solve this equation as follows:
\[
x^2 = 4
\]
\[
x = \pm 2
\]

Thus, the x-intercepts are \( x = -2 \) and \( x = 2 \).

The correct response is:
**x equals negative 2 and x equals 2.**