Which polynomial function has x-intercepts –1, 0, and 2 and passes through the point (1, –6)

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1. Answer:

   y=3x(x+1)(x-2)=3x^3-3x^2-6x

   Step-by-step explanation:

   The polynomial function can be written in the form:

   y=a(x-x1)(x-x2)(x-x3)

   where

   x1=-1

   x2=0

   x3=2

   Therefore

   y=a(x+1)(x-0)(x-2)=a(x^2+x)(x-2)=a(x^3-x^2-2x)

   To find the value for “a” we use the info about the line passing in (1,-6):

   -6=a(1-1-2)

   a=3

   y=3x(x+1)(x-2)=3x^3-3x^2-6x

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