Final answer:
The cubic function with roots at -3, -2, and 1 and a y-intercept at (0, 2) is P(x) = -1/3(x + 3)(x + 2)(x - 1).
Step-by-step explanation:
The student's question involves finding the equation of a cubic function with given roots and a y-intercept. Because the roots of the function are -3, -2, and 1, we can express the function as P(x) = k(x + 3)(x + 2)(x - 1), where k is a constant that determines the stretch/compression and orientation of the graph. To find the value of k, we use the given y-intercept (0, 2), implying P(0) = 2. Substituting the intercept into the equation gives 2 = k(0 + 3)(0 + 2)(0 - 1) = -6k, and solving for k gives us k = -1/3. Therefore, the cubic function is P(x) = -1/3(x + 3)(x + 2)(x - 1).