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

Question

down 4 units.(1 point)
Responses

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.
There are no x -intercepts.

x=−16
and x=16

Answer 1

To determine the x-intercepts of the translated function, we first need to figure out the new function after translating \( f(x) = x^2 \) down 4 units.

When we translate the function down 4 units, the new function becomes:

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

Next, we find the x-intercepts by setting the function equal to zero:

\[ x^2 - 4 = 0 \]

Now, we can factor this equation:

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

Setting each factor to zero gives us the solutions:

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

Thus, the x-intercepts of the function are:

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

So the correct response is:

x = -2 and x = 2.