Question

Match each graph to one the following functions.

$f\left(x\right)=x^2+2x+1$

Short answer

The required graph is in option A.

Step-by-step solution

Step 1. Given information.

The given function is:

$f\left(x\right)=x^2+2x+1$

It can be written as:

$f\left(x\right)=(x+1{)}^2$ $[\because (a+b{)}^2=a^2+2ab+b^2]$

Step 2. Identify the graph of the function.

The vertex of the function $f\left(x\right)=a(x-h{)}^2+k$is $(h,k)$. The graph opens up if $a>0$and it opens down if $a<0$.

In the given function $a=1,h=-1,k=0$. So, the graph must be an upward parabola with vertex at $(-1,0)$.

Step 3. Conclusion.

The required graph is in option A.