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

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 \( f(x) = x^2 \) down 4 units, we first need to express the translated function.

The original function is:

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

When we translate this function down 4 units, we get:

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

Next, we determine the x-intercepts of the function \( g(x) \) by setting it equal to zero:

\[ g(x) = 0 \]

This gives us:

\[ x^2 - 4 = 0 \]

We can solve this equation by factoring:

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

Setting each factor to zero gives 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:

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

The correct response is:

x = -2 and x = 2.