Question

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.

On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4).

Which graph represents g(x)?

On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8).
On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10).
On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).

Answer 1

g(x) = (x − 5)^2 + 1 is f(x) shifted right 5 and up 1, so its vertex is (5,1). Also f(±3)=9, so g(5±3)=9+1=10, giving points (2,10) and (8,10).

Therefore the correct graph is the one with vertex (5,1) and passing through (2,10) and (8,10) — the first option.