SOLUTION: Find a polynomial function with the zeros -6,0,3,2 whose graph passes through the point (1/2, 585)

Question 1050811: Find a polynomial function with the zeros -6,0,3,2 whose graph passes through the point (1/2, 585)
Answer by Zucchini(70) (Show Source): You can put this solution on YOUR website!
zeros: -6,0,3,2
linear factors: x(x+6)(x-3)(x-2)
Point: ( , 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 ( +6)( -3)( -2)
585= a (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.
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