Question

Determine the x-intercept(s) of the function that translates the original function f(x)=x^2 down 4 units.(1 point) Responses x=−2 and x=2 x equals negative 2 and x equals 2 There are no x-intercepts. There are no x -intercepts. x=−4 and x=4 x equals negative 4 and x equals 4 x=−16 and x=16

Answer 1

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

The original function is:
\[
f(x) = x^2
\]

After translating down 4 units, the new function becomes:
\[
g(x) = f(x) - 4 = x^2 - 4
\]

To find the x-intercepts, we set \( g(x) = 0 \):
\[
x^2 - 4 = 0
\]

Now, we can solve for \( x \):
\[
x^2 = 4
\]
Taking the square root of both sides gives us two solutions:
\[
x = 2 \quad \text{and} \quad x = -2
\]

So, the x-intercepts of the translated function are:
\[
x = -2 \quad \text{and} \quad x = 2
\]

Thus, the correct responses are:
- \( x = -2 \) and \( x = 2 \)
- x equals negative 2 and x equals 2

Both of these options are correct interpretations of the x-intercepts.