Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure.
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Question

Quizplus · Accepted Answer

The lowest-degree polynomial function with x-intercepts at (-3,0), (0,0), (2,0) and y-intercept at (0,4) is given by the formula f(x) = ax(x + 3)(x - 2) + 4, where a is a constant. Substituting (0,4) into the equation gives 4 = a(0)(3)(-2) + 4 = -6a + 4, which implies a = -1/3. Thus f(x) = (-1/3)x(x + 3)(x - 2) + 4. Expanding this equation gives f(x) = (-1/3)x^3 + x^2 + 2x + 4, which matches option D.

Write an Equation for the Lowest-Degree Polynomial Function with the Graph