Question

Determine the x-intercepts) of the function that translates the original function f(x) = x^2 down 4 units. (1 point)

A. There are no x-intercepts.

B. x = -4 and x = 4

C. x = -2 and x = 2

D. x = -16 and x = 16

Answer 1

To translate the function \( f(x) = x^2 \) down 4 units, we subtract 4 from the function:

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

To find the x-intercepts, we set \( f(x) = 0 \):

\[
x^2 - 4 = 0
\]

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

\[
x^2 = 4
\]

Taking the square root of both sides gives:

\[
x = \pm 2
\]

Thus, the x-intercepts are \( x = -2 \) and \( x = 2 \).

Therefore, the correct answer is:

C. \( x = -2 \) and \( x = 2 \)