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Cubic function

  • Thread starter brycenrg
  • Start date
  • #1
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Homework Statement


Find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0


Homework Equations


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


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 ?
 

Answers and Replies

  • #2
symbolipoint
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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".
 
  • #3
LCKurtz
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@brycenbrg: Look up the factor theorem in your text or online.
 

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