Question

The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form.

An algebra tile configuration. Only the Product spot is shown. 6 tiles are in the Product spot in 4 columns with 2 rows. First row: 1 + x squared, 1 + x. Second row: 1 + x, 3 +.
What is this function written in vertex form?

f(x) = (x + 2)2 + 3
f(x) = (x2 + 2x)2 + 3
f(x) = (x + 1)2 + 2
f(x) = (x + 3)2 + 2x

Answer 1

Complete the square:

f(x) = x^2 + 2x + 3
= (x^2 + 2x + 1) + 2
= (x + 1)^2 + 2.

So the correct choice is f(x) = (x + 1)^2 + 2 (vertex at (-1, 2)).