Find Expression for Cubic Function: f(1)=6, f(-1)=0, f(0)=f(2)=0

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SUMMARY

The discussion focuses on finding the expression for a cubic function given specific conditions: f(1)=6, f(-1)=0, and f(0)=f(2)=0. The zeros of the function are identified as x = -1, x = 0, and x = 2, leading to the factors (x + 1), x, and (x - 2). The cubic function can be expressed as f(x) = k(x + 1)x(x - 2), where k is a constant determined by substituting f(1)=6 into the equation.

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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

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The Attempt at a Solution


I tried to graph the points and find an equation for the function, but couldn't.
 
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Do you know about the relationship between zeros of a function and its factors?
 
Bohrok said:
Do you know about the relationship between zeros of a function and its factors?

yeah the factors are the zeros, right?
 
Yes. You know what values of x make the function 0, so how do you write the zeros as factors?
 
Bohrok said:
Yes. You know what values of x make the function 0, so how do you write the zeros as factors?

(x+1)(x-2)?
 
DrDanger said:
(x+1)(x-2)?

You have two; what's the last one?
 
Bohrok said:
You have two; what's the last one?
(x+6) lol I have no idea! I know it involves f(1)=6 though
 
If your cubic function has a root at x = 0 ( because f(0) = 0), might you write the factor something like (x + 0)? How would you rewrite that factor and put it with the other two factors?
 

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