If #y >0 forall x# then #p > 0# because #p# is the coeficient of #x^2# and #y(x)# cannot have #x# crossings so #y(0) = p-6 > 0#
Anyway the #x# crossings are given at
#x=(-f pm sqrt[f^2 + 24 p - 4 p^2])/(2 p)# so if
#f^2+24p-4p^2<0# no feasible crossings
or solving for #p#
#p < 1/2 (6 - sqrt[6^2 + f^2]) # and #p > 1/2 (6 + sqrt[6^2 + f^2])#
Concluding
#p > 6# and #p > 1/2 (6 + sqrt[6^2 + f^2])# or finally
#p > 1/2 (6 + sqrt[6^2 + f^2])#