Determine the x-intercept(s) of the function that translates the original function f(x)=x2 down 4 units.(1 point)

Question

Responses

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

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

There are no x-intercepts.

Answer 1

To find the x-intercepts of the function that translates the original function \( f(x) = x^2 \) down 4 units, we first need to write the translated function.

The new function after translating down by 4 units is:

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

To find the x-intercepts, we set \( g(x) \) to zero:

\[ x^2 - 4 = 0 \]

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

\[ x^2 = 4 \]

Taking the square root of both sides, we have:

\[ x = 2 \quad \text{or} \quad x = -2 \]

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

The correct response is:

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