Question

A third-degree polynomial function f has real zeros -2, ½, and 3, and its leading coefficient negative. Write an equation for f. Sketch the graph of f. How many different polynomials functions are possible for f?

Answer 1

f(x) = k(x+2)(2x-1)(x-3), where k is some constant
= k(2x^3-3x^2-11x+6)
= k(-2x^3+3x^2+11x-6)

k defines some vertical stretch, so there are an infinitely many solutions for f(x).