Question

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=−4
and x=4
x equals negative 4 and x equals 4

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

x=−16
and x=16

Answer 1

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

When a function \( f(x) \) is translated down by \( k \) units, the new function becomes:

\[
g(x) = f(x) - k
\]

In this case, the function is translated down 4 units, so we have:

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

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

\[
x^2 - 4 = 0
\]

This can be factored as:

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

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 \( g(x) = x^2 - 4 \) are:

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

The correct response is:

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