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 write the new function.

The function translated down 4 units is: \[ f(x) = x^2 - 4 \]

Next, we find the x-intercepts by setting \( f(x) = 0 \): \[ x^2 - 4 = 0 \]

We can solve this equation as follows: \[ x^2 = 4 \] \[ x = \pm 2 \]

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

The correct response is: x equals negative 2 and x equals 2.