Question

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

x=−4 and x=4

x=−2 and x=2

There are no x-intercepts.

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 translated function.

The translation down 4 units can be expressed as:

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

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

\[
x^2 - 4 = 0
\]

Now we solve for \( x \):

\[
x^2 = 4
\]

Taking the square root of both sides gives:

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

Thus, the x-intercepts of the translated function are:

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

The correct response is:

**x=−2 and x=2**