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

The new function is:

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

Next, to find the x-intercepts, we need to set \( g(x) \) equal to zero and solve for \( x \):

\[
x^2 - 4 = 0
\]

Now, we can factor the equation:

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

Setting each factor equal to zero gives us:

\[
x - 2 = 0 \quad \Rightarrow \quad x = 2
\]
\[
x + 2 = 0 \quad \Rightarrow \quad x = -2
\]

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

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

So the correct response is:

**x = −2 and x = 2**