The problem asks us to identify which of the given equations represents a family of cubic polynomials with zeros -4, 2, and 6.

1. Problem Description

The problem asks us to identify which of the given equations represents a family of cubic polynomials with zeros -4, 2, and

6.

2. Solution Steps

A polynomial has a zero at $x = r$ if and only if $(x - r)$ is a factor of the polynomial.

Since the zeros are -4, 2, and 6, the factors must be $(x - (-4))$, $(x - 2)$, and $(x - 6)$.

Therefore, the factors are $(x + 4)$, $(x - 2)$, and $(x - 6)$.

A cubic polynomial with these zeros would be of the form $y = a(x + 4)(x - 2)(x - 6)$, where $a$ is a non-zero constant.

3. Final Answer

$y = a(x + 4)(x - 2)(x - 6)$