Determine the x-intercept(s) of the function that translates the original function f(x)=x^2 down 4 units.(1 point) Responses x=−2 and x=2 x equals negative 2 and x equals 2 There are no x-intercepts. There are no x -intercepts. x=−4 and x=4 x equals negative 4 and x equals 4 x=−16 and x=16

Answer 1

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

The original function is: \[ f(x) = x^2 \]

After translating down 4 units, the new function becomes: \[ g(x) = f(x) - 4 = x^2 - 4 \]

To find the x-intercepts, we set \( g(x) = 0 \): \[ x^2 - 4 = 0 \]

Now, we can solve for \( x \): \[ x^2 = 4 \] Taking the square root of both sides gives us two solutions: \[ x = 2 \quad \text{and} \quad x = -2 \]

So, the x-intercepts of the translated function are: \[ x = -2 \quad \text{and} \quad x = 2 \]

Thus, the correct responses are:

• \( x = -2 \) and \( x = 2 \)
• x equals negative 2 and x equals 2

Both of these options are correct interpretations of the x-intercepts.