For a graph with f(x)=x^2, the vertex of the parabola is at the origin.
In the given graph, the parabola is shifted 3 units to the left and 1 unit down.
The general vertex form of a parabola is,
[tex]f(x)=a(x-h)^2+k[/tex]
Here, h is the horizontal shift and k is the vertical shift.
Since the graph is only translated and not shrinked or expanded , a=1.
Since the graph is shifted horizonatlly to the left, h is negative.
So, h=-3.
Since the graph is shifted vertically down, k is negative.
So, k=-1.
So, the equation for the given graph becomes,
[tex]\begin{gathered} f(x)=(x-(-3)^2-1 \\ f(x)=(x+3)^2-1_{} \end{gathered}[/tex]
Therefore, the function in vertex form is,
[tex]f(x)=(x+3)^2-1[/tex]
