Question

Determine the x-intercept(s) of the function that translates the original function f(x)=x2
𝑓
(
𝑥
)
=
𝑥
2
down 4 units.(1 point)
Responses

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

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

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

x=−4
𝑥
=
−
4
and x=4

Answer 1

To determine the x-intercepts of the function that translates the original function \( f(x) = x^2 \) down 4 units, we first rewrite the function after the translation.

The original function \( f(x) = x^2 \) becomes:

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

To find the x-intercepts, we set \( f(x) \) to 0 and solve for \( x \):

\[
x^2 - 4 = 0
\]

Adding 4 to both sides gives:

\[
x^2 = 4
\]

Taking the square root of both sides, we find:

\[
x = \pm 2
\]

Thus, the x-intercepts are:

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

So the correct answer is:

**x = -2 and x = 2**.