Question

Which of the following functions will have the same x-intercept(s) as its reflection about the origin?(1 point)

y=−12x+6


y=(x−4)2


y=x2


y=2x−5

Answer 1

Reflection about the origin sends f(x) to g(x)=−f(−x). The x-intercepts of g are the negatives of the x-intercepts of f, so they match exactly only when the root set is symmetric about 0.

Check each:
- y = −12x + 6 → root x = 1/2 (not symmetric)
- y = (x − 4)^2 → root x = 4 (not symmetric)
- y = x^2 → root x = 0 (symmetric)
- y = 2x − 5 → root x = 5/2 (not symmetric)

So y = x^2 is the one.