Question

Determine the x-intercept(s) of the function that translates the original function: f (x) = x^2, down 4 units.
A. x = -4, and: x = 4
B. There are no x-intercepts
C. x = -2, and: x = 2
D. x = -16, and: x = 16

Answer 1

To determine the x-intercept(s) of the function that translates \( f(x) = x^2 \) down 4 units, we first need to express this translated function mathematically.

The original function is:
\[
f(x) = x^2
\]
Translating this function down 4 units results in:
\[
g(x) = x^2 - 4
\]

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

Now, we solve for \( x \):
\[
x^2 = 4
\]
Taking the square root of both sides, we get:
\[
x = 2 \quad \text{or} \quad x = -2
\]

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

The correct answer is:
**C. x = -2, and: x = 2**