Question

What is the equation of the translated function, g(x), if
f(x) = x2?

g(x) = (x + 5)2 + 2
g(x) = (x + 2)2 + 5
g(x) = (x – 2)2 + 5
g(x) = (x – 5)2 + 2

Answer 1

I don't have the translation described, so I can't pick the single correct choice. Tell me how the parabola is shifted (left/right by how many units, up/down by how many units) and I'll pick the matching equation.

How to decide:
- For f(x) = x^2, g(x) = f(x − h) + k = (x − h)^2 + k moves the graph right h and up k.
- Thus:
- (x + 5)^2 + 2 = (x − (−5))^2 + 2 → left 5, up 2
- (x + 2)^2 + 5 → left 2, up 5
- (x − 2)^2 + 5 → right 2, up 5
- (x − 5)^2 + 2 → right 5, up 2

Tell me which shift you want (e.g., "right 5 and up 2") and I'll give the matching g(x).