Answer:
f(x) = -(x +2)(x -3)(x -12)
Step-by-step explanation:
You want the equation and a graph for a third-degree polynomial function f(x) that has real zeros -2, 12, and 3, and its leading coefficient negative.
Factors
Each zero of the function corresponds to a factor of the function that has that zero. For example, the zero at x = -2 means (x +2) is a factor of f. The leading coefficient is a multiplier of all of the factors of this form.
An equation for f(x) can be written in factored form as ...
f(x) = -(x +2)(x -3)(x -12)
Its graph is attached.
Leading coefficient
The leading coefficient is a vertical scale factor for the graph. Changing its magnitude does not change the locations of the zeros. The magnitude can be any of an infinite number of values.
There are infinitely many possible different functions for f(x).
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