Question

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

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

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

There are no x-intercepts.

Answer 1

To determine the x-intercepts of the translated function, we first need to define the new function after translating \( f(x) = x^2 \) down 4 units.

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

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

Next, we find the x-intercepts by setting \( g(x) \) equal to zero:

\[
x^2 - 4 = 0
\]

Now, we can solve for \( x \):

\[
x^2 = 4
\]

Taking the square root of both sides gives us:

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

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

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

So the answer is:

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