Question

determine the x-intercept(s) of the function that translates the orginal function f(x)=x^2 down 4 units
a there are no x-intercepts
b x=-2 and x=2
c x==16 and x=16
d x=-4 and x=4

Answer 1

To determine the x-intercepts of the function that translates the original function \( f(x) = x^2 \) down 4 units, we first need to write the translated function.

The translation down by 4 units can be expressed mathematically as:

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

Next, to find the x-intercepts of the function \( g(x) \), we set \( g(x) = 0 \):

\[
x^2 - 4 = 0
\]

Now, we solve for \( x \):

\[
x^2 = 4
\]

Taking the square root of both sides, we get:

\[
x = \pm 2
\]

Thus, the x-intercepts of the function \( g(x) = x^2 - 4 \) are:

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

The correct answer is:

**b. \( x = -2 \) and \( x = 2 \)**.