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

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

Answer 1

To find the x-intercept(s) of the function that translates \( f(x) = x^2 \) down 4 units, we first need to write the new function after the translation.

The new function is:

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

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

\[ x^2 - 4 = 0 \]

Now, we can factor the equation:

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

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 \( g(x) \) are:

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

So the correct response is:

x = −2 and x = 2