Let h,hM : Fnq → Fq be quadratic forms with h not degenerate. Fix k ∊ Fq and set Cn(k,h)Fq := {h(x1, . . . ,xn) = k} = Fnq. We compute (in many cases) the image of hMCn (k,h)Fq . This question is related to a question on the numerical range of matrices over a finite field.