Question

Question

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

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

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

x=−16
and x=16

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 determine the equation of the translated function.

When a function \( f(x) \) is translated down by \( k \) units, the new function becomes:

\[ g(x) = f(x) - k \]

In this case, the function is translated down 4 units, so we have:

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

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

\[ x^2 - 4 = 0 \]

This can be factored as:

\[ (x - 2)(x + 2) = 0 \]

Setting each factor equal to zero gives us:

\[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \]

\[ x + 2 = 0 \quad \Rightarrow \quad x = -2 \]

Thus, the x-intercepts of the function \( g(x) = x^2 - 4 \) are:

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

The correct response is:

x = -2 and x = 2.