Write the equation of the quadratic function in standard form represented by the graph

Vertex is at (-3,-1) so expressing the quadratic function in vertex form:

f(x) = a(x -(-3))^2 + (-1)

= a(x+3)^2 -1

also note when x=0, f(0)=8

8 = a(3)^2 -1 = 9a-1

so a=1

f(x) = (x+3)^2 - 1

= x^2 + 6x + 9 -1

= x^2 +6x + 8