Question

The graph of f(x) = x2 is translated to form
g(x) = (x – 2)2 – 3.

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 (0, 1), has a vertex at (2, negative 3), and goes through (4, 1).
On a coordinate plane, a parabola opens up. It goes through (negative 3, 4), has a vertex at (negative 2, 3), and goes through (negative 1, 4).
On a coordinate plane, a parabola opens up. It goes through (1, 4), has a vertex at (2, 3), and goes through (3, 4).
On a coordinate plane, a parabola opens up. It goes through (negative 4, 1), has a vertex at (negative 2, negative 3), and goes through (0, 1).

Answer 1

The first graph. g(x) = (x−2)^2 − 3 is f(x) shifted right 2 and down 3, so the vertex is at (2, −3) and the former points (−2,4) and (2,4) become (0,1) and (4,1) — which matches the first graph.