Answer
$y=(x+3)^2-4$
Work Step by Step
We know that, "the graph $y=f(x)$ shifted left $h$ units is $y=f(x+h)$ and the graph $y=f(x)$ shifted down $k$ units is $y=f(x)-k$".
Here we have $f(x)=x^2$
Since the graph of $f(x)=x^2$ is shifted $3$ units left, then the resulting function is $g(x)=(x+3)^2$.
The new function is then shifted down $4$ units is the resulting function is $h(x)=(x+3)^2-4$.
Therefore, the answer us $y=(x+3)^2-4$.
