SOLUTION: Write the equation of the cubic function f(x), if f(-2)=0, f(1)=0, f(3)=0 and f(6)=8

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Question 427637: Write the equation of the cubic function f(x), if f(-2)=0, f(1)=0, f(3)=0 and f(6)=8
Answer by Gogonati(855) About Me  (Show Source):
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Solution:Since the zeros of the function are:-2, 1, and 3 the cubic function will be:
f%28x%29=%28x%2B2%29%28x-1%29%28x-3%29=%28x%5E2%2Bx-2%29%28x-3%29=x%5E3-2x%5E2-5x%2B6
The value of this function for x=6 is f(6)=120. The problem request to find a function that g(6)=8, 8=120-112, therefore the requested function will be:
g%28x%29=x%5E3-2x%5E2-5x-106, where g(6)=8.