Answer
$f(x)=x^2-3$
Work Step by Step
Given the standard function, $
f(x)=x^2
$, the equation of the graph that shifts downward will have a negative constant added to the equation. Hence, a shift of $3$ units downward will have the equation,
\begin{array}{l}\require{cancel}
f(x)=x^2-3
.\end{array}