Question

Which is the graph of f(x) = x2 – 2x + 3?

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

Answer 1

The first graph.

Reason: f(x) = x^2 − 2x + 3 = (x − 1)^2 + 2, so the vertex is (1, 2) and the parabola opens upward. Also f(0)=3 and f(2)=3, so it goes through (0,3) and (2,3).