Question

Which is the graph of the function f(x) = x2 + 2x + 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 (1, 2), and goes through (2, 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).
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).

Answer 1

The first graph.

Reason: f(x)=x^2+2x+3 has vertex at x = -b/(2a) = -2/2 = -1, and f(-1)=1-2+3=2 so vertex (-1,2). Also f(0)=3 and f(-2)=3, so it passes through (0,3) and (-2,3). That matches the first description.