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=−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

Answer 1

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

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

Next, we find the x-intercepts by setting \( g(x) = 0 \):

\[ x^2 - 4 = 0 \]

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

\[ x^2 = 4 \]

Taking the square root of both sides:

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

Thus, the x-intercepts of the translated function \( g(x) \) are:

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

So, the correct answer is:

x = −2 and x = 2.