Question 1050811
zeros: -6,0,3,2

linear factors: x(x+6)(x-3)(x-2)

Point: ({{{1/2}}} , 585)

f(x)= ax(x+6)(x-3)(x-2)
(the a is there because we don't know if there will be a vertical stretch or shrink)

Plug in what you know:

585= a {{{1/2}}}({{{1/2}}} +6)({{{1/2}}} -3)({{{1/2}}} -2)
585= a {{{1/2}}}(6.5)(-2.5)(-1.5)
585= a 12.1875
48= a

Polynomial function: f(x) = 48x(x+6)(x-3)(x-2)

If your teacher prefers you to multiply it out, I'm sure you can take it from here.