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

Question

down 4 units.(1 point)
Responses

There are no x-intercepts.
There are no x -intercepts.

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

x=−16
and x=16
x equals negative 3.464 and x equals 3.464

x=−4
and x=4

Answer 1

To determine the x-intercepts of the function that translates \( f(x) = x^2 \) down 4 units, we first need to identify the new function after the translation.

The original function is: \[ f(x) = x^2 \]

When we translate it down 4 units, the new function becomes: \[ g(x) = f(x) - 4 = x^2 - 4 \]

To find the x-intercepts, we set the function equal to zero: \[ g(x) = 0 \] \[ x^2 - 4 = 0 \]

Now, we can solve for \( x \): \[ x^2 = 4 \]

Taking the square root of both sides, we get: \[ x = \pm 2 \]

Thus, the x-intercepts are: \[ x = -2 \quad \text{and} \quad x = 2 \]

The correct response is: x=−2 and x=2.