Answer:
f(x) = -3x(x +1)(x -2)
Explanation:
You want a cubic function with zeros at x=-1, 0, 2, that passes through point f(1) = 6.
Factors
Each zero x = p corresponds to a factor (x -p). The factored form of the required function is ...
f(x) = a(x +1)(x -0)(x -2)
Scale factor
The value of f(1) is ...
f(1) = a(1 +1)(1 -0)(1 -2) = -2a = 6
a = -3
Function
Then the desired function is ...
f(x) = -3x(x +1)(x -2)
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Additional comment
In expanded form, the function is ...
f(x) = -3x³ +3x² +6x
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