Answer
$f(x)=4(x-2)^2-3$
Work Step by Step
The vertex equation of a parabola is given as:
$f(x)=a(x-h)^2+k$
Here, $(h,k)$ represents vertex.
Given: Vertex: $(h,k)=(2,-3)$
At point $(3,1)$ ,
Thus, we have $f(x)=a(x-2)^2-3$
and $1=a(3-2)^2-3 \implies a=4$
Thus, the vertex equation of a parabola is:
$f(x)=4(x-2)^2-3$
