Work Step by Step
Since $x^2+2x+1=(x+1)^2$, the given function can be written as: $f(x) =(x+1)^2$ RECALL: (1) The vertex form of a quadratic function whose vertex is at $(h, k)$ is: $f(x) = a(x-h)^2+k$ (2) The graph of the quadratic function $ax^2+bx+c$ is a parabola that opens: (i) upward when $a \gt 0$; (ii) downward when $a\lt 0$. Using the vertex form in (1) above, the given function has its vertex at $(-1,0)$. Using the rule in (2) above, with $a=1$, the given function's graph is a parabola that opens upward. The parabola that opens upward and whose vertex is at $(-1, 0)$ is the one in Option (A).