Question

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
x equals negative 4 and x equals 4
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Answer 1

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

The original function \( f(x) = x^2 \) translated down 4 units is represented mathematically as:
\[
g(x) = x^2 - 4
\]

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

Next, we can factor the equation:
\[
(x - 2)(x + 2) = 0
\]

Setting each factor equal to zero gives us:
1. \( x - 2 = 0 \) which implies \( x = 2 \)
2. \( x + 2 = 0 \) which implies \( x = -2 \)

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

**The correct response is**: x = -2 and x = 2.