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

Question

down 4 units.(1 point)
Responses

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

x=−4
and x=4
x equals negative 4 and x equals 4

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

There are no x-intercepts.

Answer 1

To determine the x-intercepts of the function \( f(x) = x^2 \) translated down 4 units, we first find the new function after the translation.

The original function is: \[ f(x) = x^2 \] Translating down 4 units gives us: \[ f(x) = x^2 - 4 \]

Now, to find the x-intercepts, we set \( f(x) \) equal to zero: \[ x^2 - 4 = 0 \] This can be factored as: \[ (x - 2)(x + 2) = 0 \]

Setting each factor to zero gives:

1. \( x - 2 = 0 \) ⟹ \( x = 2 \)
2. \( x + 2 = 0 \) ⟹ \( x = -2 \)

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

So the correct response is: x equals negative 2 and x equals 2.