Answer
The possible equation for the graph is $y={{\left( x+1 \right)}^{2}}-4$.
Work Step by Step
The given graph looks similar to $y={{x}^{2}}$ but the function $y={{x}^{2}}$ passes through the origin and is symmetric about the y axis. So this graph must be shifted.
Now the given graph is vertically shifted downwards on the $y$ axis by 4 units.
Thus the equation of the graph can be written as,
$y={{x}^{2}}-4$
Also the graph is shifted to the left by 1 unit; thus the variable $x$ is replaced by a factor of $x+1$.
So, the equation is:
$y={{\left( x+1 \right)}^{2}}-4$
Hence, the possible function is $y={{\left( x+1 \right)}^{2}}-4$.
