Determine the x-intercept(s) of the function that translates the original function f(x)=x2

Question

down 4 units.(1 point)
Responses

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

x=−2
and x=2
x equals negative 2 and x equals 2

There are no x-intercepts.

Answer 1

The original function is \( f(x) = x^2 \).

To translate this function down 4 units, we subtract 4 from the function:

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

To find the x-intercepts, we set the function equal to zero:

\[ x^2 - 4 = 0 \]

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

\[ x^2 = 4 \]

Taking the square root of both sides gives:

\[ x = \pm 2 \]

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

Thus, the correct response is:

x equals negative 2 and x equals 2.