Final answer:
The polynomial is constructed using the supplied zeros and y-intercept, resulting in an equation of the form f(x) = a(x + 3)(x + 2)(x - 1), and determining the coefficient a with the y-intercept -10.
Step-by-step explanation:
The question asks us to form a third-degree polynomial with given zeros and a specific y-intercept. A polynomial of degree three, which has zeros of -3, -2, and 1, can be represented as f(x) = a(x + 3)(x + 2)(x - 1), where a is a nonzero constant.
To find the y-intercept of -10, we substitute x = 0 into the polynomial to get f(0) = a(0 + 3)(0 + 2)(0 - 1) = -10, which gives us the value of a. To get the requested polynomial, we solve for a and expand the product.
The complete question is: What is the 3rd degree polynomial function whose zeros are -3, 2, and ½?