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

Question

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

Answer 1

To find the x-intercepts of the function that results from translating the original function \( f(x) = x^2 \) down 4 units, we first express the new function after the translation.

The new function after translating \( f(x) \) down 4 units is:

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

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

\[ x^2 - 4 = 0 \]

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

\[ x^2 = 4 \]

Taking the square root of both sides:

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

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

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

The correct response from the options provided is:

x equals negative 2 and x equals 2.