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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial function with the zeros -6,0,3,2 whose graph passes through the point (1/2, 585)      Log On


   

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) About Me  (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: (1%2F2 , 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%2F2(1%2F2 +6)(1%2F2 -3)(1%2F2 -2)
585= a 1%2F2(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.