Question

What do you notice about the vertex and the line of symmetry for this equations y = x2 + 4x + 1?

Answer 1

The vertex intersects the line of symmetry. Also x = line of symmetry.

Answer 2

indeed, the vertex intersects the line of symmetry.
\[y=x^2+4x+1 = (x+2)^2 - 3\]
which is a minimum at
\[x=-2\]
this being the x-coordinate of the vertex. Since the parabola is the same shape either side of the vertex, we have that the line of symmetry is
\[x=-2\]