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Cubic function

  1. Aug 26, 2013 #1
    1. The problem statement, all variables and given/known data
    Find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0

    2. Relevant equations
    I figured it out but im not sure why we use the equation f(x) = a[x-(-1)](x-0)(x-2)

    3. The attempt at a solution
    Im assuming its because if u times that equation that is a cubic function, but does it have anything todo with f(-1)=f(0)=f(2)=0 ?
  2. jcsd
  3. Aug 26, 2013 #2


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    Certainly yes. Those f(c)=0 values mean that some binomial, x-c, is a factor of the function's expression or its definition. Your exercise gives you three of them and they are for a cubic function. The binomial factors will take care of your roots for your function. The coefficient, "a", is for accounting for the remainder in case you choose a value for x which is not a root. The given f(1)=6 helps you to find "a".
  4. Aug 26, 2013 #3


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    @brycenbrg: Look up the factor theorem in your text or online.
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