Determine the x-intercept(s) of the function that translates the original function f(x)=x2

Question

𝑓
(
𝑥
)
=
𝑥
2
down 4 units.(1 point)
Responses

x=−4
𝑥
=
−
4
and x=4
𝑥
=
4
x equals negative 4 and x equals 4

x=−2
𝑥
=
−
2
and x=2
𝑥
=
2
x equals negative 2 and x equals 2

x=−16
𝑥
=
−
16
and x=16
𝑥
=
16
x equals negative 3.464 and x equals 3.464

There are no x-intercepts.

Answer 1

To determine the x-intercepts of the function \( f(x) = x^2 - 4 \) (which is the result of translating \( f(x) = x^2 \) down 4 units), we need to find where the function equals zero:

\[ f(x) = x^2 - 4 = 0 \]

Solving this equation:

1. Add 4 to both sides: \[ x^2 = 4 \]

2. Take the square root of both sides: \[ x = \pm 2 \]

Thus, the x-intercepts are \( x = -2 \) and \( x = 2 \).

The correct answer is:

x = −2 and x = 2.